pwc-archive/papers-with-abstracts huggingface dataset:
Evaluating the Financial Market Function in Prewar Japan using a Time-Varying Parameter Model
Authors: Kenichi Hirayama, Akihiko Noda
Date: 2020-08-03 00:00:00
Tasks: Form

This paper explores when the financial market lost the price formation function in prewar Japan in the sense of Fama's (1970) semi-strong form market efficiency using a new dataset. We particularly focus on the relationship between the prewar Japanese financial market and several government policy interventions to explore whether the semi-strong form market efficiency evolves over time. To capture the long-run impact of government policy interventions against the markets, we measure the time-varying joint degree of market efficiency and the time-varying impulse responses based on Ito et al.'s (2014; 2017) generalized least squares-based time-varying vector autoregressive model. The empirical results reveal that (1) the joint degree of market efficiency in the prewar Japanese financial market fluctuated over time because of external events such as policy changes and wars, (2) the semi-strong form EMH is almost supported in the prewar Japanese financial market, (3) Lo's (2004) adaptive market hypothesis is supported in the prewar Japanese financial market even if we consider that the public information affects the financial markets, and (4) the prewar Japanese financial markets lost the price formation function in 1932 and that was a turning point in the market.
Non-Linear Discounting and Default Compensation: Valuation of Non-Replicable Value and Damage: When the Social Discount Rate may become Negative
Authors: Christian P. Fries
Date: 2020-07-13 00:00:00

In this paper, we introduce a model that adds a non-linearity to discounting: the discounting factor may depend on the notional (i.e., discounted values are no longer linear in the notional). In the first part of the paper, we provide a discounting when discount factors cannot be derived from market products. That is, a risk-neutralising trading strategy cannot be performed. This is the case when one needs a risk-free (default-free) discounting, but default protection on funding providers is not traded. For this case, we derive a default compensation factor that describes the present value of a strategy to compensate for default (like buying default protection would do). In a second part of the paper, we introduce a model where the survival probability, and hence the discount factor, depends on the notional. This model introduces an effect not present in the classical modelling of a time-dependent survival probability. Our model allows that large liquidity requirements are more likely to default instantly than small ones. Combined, the two models build a framework where discounting (and hence valuation) is non-linear: discount factors depend on the amount to be discounted. Our approach builds on top of the classical theory of discounting (which may either be given as market-implied or be derived from a model of utility, consumption and production). In that sense, it is rather a generalisation than an alternative. The modelling approach has specific relevance for climate models, where discounting is an important aspect in assessing the severity of future events. Our model may result in non-decaying discount factors (negative discount rates) for certain scenarios.
On the harmonic mean representation of the implied volatility
Authors: Stefano De Marco
Date: 2020-07-07 00:00:00

It is well know that, in the short maturity limit, the implied volatility approaches the integral harmonic mean of the local volatility with respect to log-strike, see [Berestycki et al., Asymptotics and calibration of local volatility models, Quantitative Finance, 2, 2002]. This paper is dedicated to a complementary model-free result: an arbitrage-free implied volatility in fact is the harmonic mean of a positive function for any fixed maturity. We investigate the latter function, which is tightly linked to Fukasawa's invertible map $f_{1/2}$ [Fukasawa, The normalizing transformation of the implied volatility smile, Mathematical Finance, 22, 2012], and its relation with the local volatility surface. It turns out that the log-strike transformation $z = f_{1/2}(k)$ defines a new coordinate system in which the short-dated implied volatility approaches the arithmetic (as opposed to harmonic) mean of the local volatility. As an illustration, we consider the case of the SSVI parameterization: in this setting, we obtain an explicit formula for the volatility swap from options on realized variance.
Repo Haircuts and Economic Capital: A Theory of Repo Pricing
Authors: Wujiang Lou
Date: 2016-04-19 00:00:00

A repurchase agreement lets investors borrow cash to buy securities. Financier only lends to securities' market value after a haircut and charges interest. Repo pricing is characterized with its puzzling dual pricing measures: repo haircut and repo spread. This article develops a repo haircut model by designing haircuts to achieve high credit criteria, and identifies economic capital for repo's default risk as the main driver of repo pricing. A simple repo spread formula is obtained that relates spread to haircuts negative linearly. An investor wishing to minimize all-in funding cost can settle at an optimal combination of haircut and repo rate. The model empirically reproduces repo haircut hikes concerning asset backed securities during the financial crisis. It explains tri-party and bilateral repo haircut differences, quantifies shortening tenor's risk reduction effect, and sets a limit on excess liquidity intermediating dealers can extract between money market funds and hedge funds.
Analysis on the Pricing model for a Discrete Coupon Bond with Early redemption provision by the Structural Approach
Authors: Hyong Chol O, Tae Song Kim
Date: 2020-07-03 00:00:00

In this paper, using the structural approach is derived a mathematical model of the discrete coupon bond with the provision that allow the holder to demand early redemption at any coupon dates prior to the maturity and based on this model is provided some analysis including min-max and gradient estimates of the bond price. Using these estimates the existence and uniqueness of the default boundaries and some relationships between the design parameters of the discrete coupon bond with early redemption provision are described. Then under some assumptions the existence and uniqueness of the early redemption boundaries is proved and the analytic formula of the bond price is provided using higher binary options. Finally for our bond is provided the analysis on the duration and credit spread, which are used widely in financial reality. Our works provide a design guide of the discrete coupon bond with the early redemption provision
Some pricing tools for the Variance Gamma model
Authors: Jean-Philippe Aguilar
Date: 2019-12-12 00:00:00
Tasks: model

We establish several closed pricing formula for various path-independent payoffs, under an exponential L\'evy model driven by the Variance Gamma process. These formulas take the form of quickly convergent series and are obtained via tools from Mellin transform theory as well as from multidimensional complex analysis. Particular focus is made on the symmetric process, but extension to the asymmetric process is also provided. Speed of convergence and comparison with numerical methods (Fourier transform, quadrature approximations, Monte Carlo simulations) are also discussed; notable feature is the accelerated convergence of the series for short term options, which constitutes an interesting improvement of numerical Fourier inversion techniques.
A closed formula for illiquid corporate bonds and an application to the European market
Authors: Roberto Baviera, Aldo Nassigh, Emanuele Nastasi
Date: 2019-01-21 00:00:00
Tasks: Position

We propose an option approach for pricing bond illiquidity that is reminiscent of the celebrated work of Longstaff (1995) on the non-marketability of some non-dividend-paying shares in IPOs. This approach describes a quite common situation in the fixed income market: it is rather usual to find issuers that, besides liquid benchmark bonds, issue some other bonds that either are placed to a small number of investors in private placements or have a limited issue size. We model interest rate and credit risks via a convenient reduced-form approach. We deduce a simple closed formula for illiquid corporate coupon bond prices when liquid bonds with similar characteristics (e.g. maturity) are present in the market for the same issuer. The key model parameter is the time-to-liquidate a position, i.e. the time that an experienced bond trader takes to liquidate a given position on a corporate coupon bond. We show that illiquid bonds present an additional liquidity spread that depends on the time-to-liquidate aside from bond volatility. We provide a detailed application for two issuers in the European market.
Nonparametric Pricing and Hedging of Volatility Swaps in Stochastic Volatility Models
Authors: Frido Rolloos
Date: 2020-01-08 00:00:00

In this paper the zero vanna implied volatility approximation for the price of freshly minted volatility swaps is generalised to seasoned volatility swaps. We also derive how volatility swaps can be hedged using a strip of vanilla options with weights that are directly related to trading intuition. Additionally, we derive first and second order hedges for volatility swaps using only variance swaps. As dynamically trading variance swaps is in general cheaper and operationally less cumbersome compared to dynamically rebalancing a continuous strip of options, our result makes the hedging of volatility swaps both practically feasible and robust. Within the class of stochastic volatility models our pricing and hedging results are model-independent and can be implemented at almost no computational cost.
Tax- and expense-modified risk-minimization for insurance payment processes
Authors: Kristian Buchardt, Christian Furrer, Thomas Møller
Date: 2019-07-09 00:00:00

We study the problem of determining risk-minimizing investment strategies for insurance payment processes in the presence of taxes and expenses. We consider the situation where taxes and expenses are paid continuously and symmetrically and introduce the concept of tax- and expense-modified risk-minimization. Risk-minimizing strategies in the presence of taxes and expenses are derived and linked to Galtchouk-Kunita-Watanabe decompositions associated with modified versions of the original payment processes. Furthermore, we show equivalence to an alternative approach involving an artificial market consisting of after-tax and after-expense assets, and we establish a type of consistency with classic risk-minimization. Finally, a case study involving classic multi-state life insurance payments in combination with a bond market exemplifies the results.
Model independent WWR for regulatory CVA and for accounting CVA and FVA
Authors: Chris Kenyon, Mourad Berrahoui, Benjamin Poncet
Date: 2020-03-06 00:00:00

General wrong way risk (WWR) estimation is necessary for regulatory CVA capital and useful for pricing CVA and FVA. We introduce a model independent method for calculating WWR and update the definition of WWR to deal with the lack of replication instruments (calibration data) transparently. This model independent approach is extremely simple: we just re-write the CVA and FVA integral expressions in terms of their components and then calibrate these components. This provides transparency between component calibration and CVA/FVA effect because there is no model interpretation in between. Including funding in WWR means that there are now two WWR terms rather than the usual one. Using a regulatory inspired calibration from MAR50 we investigate WWR effects for vanilla interest rate swaps and show that the WWR effects for FVA are significantly more material than for CVA. This model independent approach can also be used to compare any WWR model by simply calibrating to it for a portfolio and counterparty, to demonstrate the effects of the model under investigation in terms of components of CVA/FVA calculations.
Efficient representation of supply and demand curves on day-ahead electricity markets
Authors: Mariia Soloviova, Tiziano Vargiolu
Date: 2020-02-02 00:00:00

Our paper aims to model supply and demand curves of electricity day-ahead auction in a parsimonious way. Our main task is to build an appropriate algorithm to present the information about electricity prices and demands with far less parameters than the original one. We represent each curve using mesh-free interpolation techniques based on radial basis function approximation. We describe results of this method for the day-ahead IPEX spot price of Italy.
Using Networks and Partial Differential Equations to Predict Bitcoin Price
Authors: Yufang Wang, HaiYan Wang
Date: 2020-01-08 00:00:00

Over the past decade, the blockchain technology and its Bitcoin cryptocurrency have received considerable attention. Bitcoin has experienced significant price swings in daily and long-term valuations. In this paper, we propose a partial differential equation (PDE) model on the bitcoin transaction network for predicting bitcoin price. Through analysis of bitcoin subgraphs or chainlets, the PDE model captures the influence of transaction patterns on bitcoin price over time and combines the effect of all chainlet clusters. In addition, Google Trends Index is incorporated to the PDE model to reflect the effect of bitcoin market sentiment. The experiment shows that the average accuracy of daily bitcoin price prediction is 0.82 for 362 consecutive days in 2017. The results demonstrate the PDE model is capable of predicting bitcoin price. The paper is the first attempt to apply a PDE model to the bitcoin transaction network for predicting bitcoin price.
Quantization goes Polynomial
Authors: Giorgia Callegaro, Lucio Fiorin, Andrea Pallavicini
Date: 2017-10-31 00:00:00
Tasks: Quantization

Quantization algorithms have been successfully adopted to option pricing in finance thanks to the high convergence rate of the numerical approximation. In particular, very recently, recursive marginal quantization has been proven to be a flexible and versatile tool when applied to stochastic volatility processes. In this paper we apply for the first time quantization techniques to the family of polynomial processes, by exploiting their peculiar nature. We focus our analysis on the stochastic volatility Jacobi process, by presenting two alternative quantization procedures: the first is a new discretization technique, whose foundation lies on the polynomial structure of the underlying process and which is suitable for vanilla option pricing, the second is based on recursive marginal quantization and it allows for pricing of (vanilla and) exotic derivatives. We prove theoretical results to assess the induced approximation errors, and we describe in numerical examples practical tools for fast vanilla and exotic option pricing.
On Extensions of the Barone-Adesi & Whaley Method to Price American-Type Options
Authors: Ludovic Mathys
Date: 2019-12-01 00:00:00

The present article provides an efficient and accurate hybrid method to price American standard options in certain jump-diffusion models as well as American barrier-type options under the Black & Scholes framework. Our method generalizes the quadratic approximation scheme of Barone-Adesi & Whaley (1987) and several of its extensions. Using perturbative arguments, we decompose the early exercise pricing problem into sub-problems of different orders and solve these sub-problems successively. The obtained solutions are combined to recover approximations to the original pricing problem of multiple orders, with the 0-th order version matching the general Barone-Adesi & Whaley ansatz. We test the accuracy and efficiency of the approximations via numerical simulations. The results show a clear dominance of higher order approximations over their respective 0-th order version and reveal that significantly more pricing accuracy can be obtained by relying on approximations of the first few orders. Additionally, they suggest that increasing the order of any approximation by one generally refines the pricing precision, however that this happens at the expense of greater computational costs.
Option pricing under normal dynamics with stochastic volatility
Authors: Matta Uma Maheswara Reddy
Date: 2019-09-17 00:00:00

In this paper, we derive the price of a European call option of an asset following a normal process assuming stochastic volatility. The volatility is assumed to follow the Cox Ingersoll Ross (CIR) process. We then use the fast Fourier transform (FFT) to evaluate the option price given we know the characteristic function of the return analytically. We compare the results of fast Fourier transform with the Monte Carlo simulation results of our process. Further, we present a numerical example to understand the normal implied volatility of the model.
A New Set of Financial Instruments
Authors: Abootaleb Shirvani, Stoyan V. Stoyanov, Svetlozar T. Rachev, Frank J. Fabozzi
Date: 2016-12-02 00:00:00

In complete markets, there are risky assets and a riskless asset. It is assumed that the riskless asset and the risky asset are traded continuously in time and that the market is frictionless. In this paper, we propose a new method for hedging derivatives assuming that a hedger should not always rely on trading existing assets that are used to form a linear portfolio comprised of the risky asset, the riskless asset, and standard derivatives, but rather should design a set of specific, most-suited financial instruments for the hedging problem. We introduce a sequence of new financial instruments best suited for hedging jump-diffusion and stochastic volatility market models. The new instruments we introduce are perpetual derivatives. More specifically, they are options with perpetual maturities. In a financial market where perpetual derivatives are introduced, there is a new set of partial and partial-integro differential equations for pricing derivatives. Our analysis demonstrates that the set of new financial instruments together with a risk measure called the tail-loss ratio measure defined by the new instrument's return series can be potentially used as an early warning system for a market crash.
Optimal portfolios with anticipating information on the stochastic interest rate
Authors: Bernardo D'Auria, José Antonio Salmerón
Date: 2017-11-09 00:00:00
Tasks: Portfolio Optimization

By employing the technique of enlargement of filtrations, we demonstrate how to incorporate information about the future trend of the stochastic interest rate process into a financial model. By modeling the interest rate as an affine diffusion process, we obtain explicit formulas for the additional expected logarithmic utility in solving the optimal portfolio problem. We begin by solving the problem when the additional information directly refers to the interest rate process, and then extend the analysis to the case where the information relates to the values of an underlying Markov chain. The dynamics of this chain may depend on anticipated market information, jump at predefined epochs, and modulate the parameters of the stochastic interest rate process. The theoretical study is then complemented by an illustrative numerical analysis.
Risk-Control Strategies
Authors: Patrice Gaillardetz, Saeb Hachem
Date: 2019-08-06 00:00:00

In this paper, we consider the pricing of derivative products that involve dynamic hedging strategies and payments within the planning horizon. Equity-indexed annuities (EIAs), Guaranteed investment certificate (GIC), American and Barrier options are typical examples of these products. Our exploration involves evaluation under different assumptions related to the way the risk is tailored by the issuer. The unified constrained discrete stochastic dynamic programming framework presented in this paper makes use of sequential local minimizing strategies related to stochastic transitions. This sequential minimizations takes into account all intermediate requirements and involves several dynamic risk measures modelling. To demonstrate the flexibility of this framework we present numerical examples featuring GICs and point-to-point EIAs.
Decomposition formula for rough Volterra stochastic volatility models
Authors: Raul Merino, Jan Pospíšil, Tomáš Sobotka, Tommi Sottinen, Josep Vives
Date: 2019-06-17 00:00:00

The research presented in this article provides an alternative option pricing approach for a class of rough fractional stochastic volatility models. These models are increasingly popular between academics and practitioners due to their surprising consistency with financial markets. However, they bring several challenges alongside. Most noticeably, even simple non-linear financial derivatives as vanilla European options are typically priced by means of Monte-Carlo (MC) simulations which are more computationally demanding than similar MC schemes for standard stochastic volatility models. In this paper, we provide a proof of the prediction law for general Gaussian Volterra processes. The prediction law is then utilized to obtain an adapted projection of the future squared volatility -- a cornerstone of the proposed pricing approximation. Firstly, a decomposition formula for European option prices under general Volterra volatility models is introduced. Then we focus on particular models with rough fractional volatility and we derive an explicit semi-closed approximation formula. Numerical properties of the approximation for a popular model -- the rBergomi model -- are studied and we propose a hybrid calibration scheme which combines the approximation formula alongside MC simulations. This scheme can significantly speed up the calibration to financial markets as illustrated on a set of AAPL options.
Hedging crop yields against weather uncertainties -- a weather derivative perspective
Authors: Samuel Asante Gyamerah, Philip Ngare, Dennis Ikpe
Date: 2019-05-18 00:00:00
Tasks: Management

The effects of weather on agriculture in recent years have become a major global concern. Hence, the need for an effective weather risk management tool (i.e., weather derivatives) that can hedge crop yields against weather uncertainties. However, most smallholder farmers and agricultural stakeholders are unwilling to pay for the price of weather derivatives (WD) because of the presence of basis risks (product-design and geographical) in the pricing models. To eliminate product-design basis risks, a machine learning ensemble technique was used to determine the relationship between maize yield and weather variables. The results revealed that the most significant weather variable that affected the yield of maize was average temperature. A mean-reverting model with a time-varying speed of mean reversion, seasonal mean, and local volatility that depended on the local average temperature was then proposed. The model was extended to a multi-dimensional model for different but correlated locations. Based on these average temperature models, pricing models for futures, options on futures, and basket futures for cumulative average temperature and growing degree-days are presented. Pricing futures on baskets reduces geographical basis risk, as buyers have the opportunity to select the most appropriate weather stations with their desired weight preference. With these pricing models, farmers and agricultural stakeholders can hedge their crops against the perils of extreme weather.