TMU Workshop on Finance 2024
September 26, 2024 (Thu) 12:50–18:00
September 27, 2024 (Fri) 13:00–18:10

Marunouchi Satellite Campus, Tokyo Metropolitan University, Tokyo, Japan

Plenary Speakers
Jie Yen Fan
Monash University
Andrea Macrina
University College London
Tai-Ho Wang
The City University of New York
Kazutoshi Yamazaki University of Queensland

Speakers
Rusudan Kevkhishvili Kyoto University
Kiichi Kitajima
Mitsubishi UFJ Trust Investment Technology InstituteTomohiro Koike
Kyoto University
Wataru Nozawa
Fukuoka University
Benjamin Poignard
Osaka University
Makoto Shimoshimizu Tokyo University of Science
Takaaki Shiotani
The University of Tokyo
Ryoichi Suzuki
Ritsumeikan University
Ryoji Takano
Osaka University
Kohta Takehara
Tokyo Metropolitan University
Yuma Tamura
Ritsumeikan University
Tomooki Yuasa
Tokyo Metropolitan University

Scientiﬁc Committee
Takanori Adachi
Tokyo Metropolitan University
Yukio Muromachi
Tokyo Metropolitan University
Kohta Takehara
Tokyo Metropolitan University
Tomonori Uchiyama Tokyo Metropolitan University
Kyoko Yagi
Tokyo Metropolitan University
Toshinao Yoshiba
Tokyo Metropolitan University
Tomooki Yuasa
Tokyo Metropolitan University

Organized by Research Center for Quantitative Finance, Tokyo Metropolitan University
Supported by Institute of Economic Research, Kyoto University

September 26 (Thu)
12:50–13:00

Opening address by Tomonori Uchiyama, Director of Research Center for
Quantitative Finance, Tokyo Metropolitan University

Session 1 Chair: Kazutoshi Yamazaki, University of Queensland
13:00–13:45 Tai-Ho Wang
The City University of New York
“Relative entropy-regularized robust optimal order execution under transient
impact”
13:45–14:15

Kiichi Kitajima
Mitsubishi UFJ Trust Investment Technology Institute“High-Frequency Trading and Risk Sharing Capacity in Market Making with
Asymmetric Information”

14:15–14:45

Tomooki Yuasa
Tokyo Metropolitan University“Randomized multi-factor approximation for stochastic volterra equations withfractional kernel”

Session 2 Chair: Andrea Macrina, University College London
15:00–15:45 Jie Yen Fan
Monash University“From mimicking to local Brownian motions”
15:45–16:15

Yuma Tamura
Ritsumeikan University“Formulas for ”delta” of the options whose underlying asset prices are given
by aﬃne processes”

16:15–16:45

Ryoji Takano
Osaka University“Large deviation principle for rough volatility models”

Session 3 Chair: Takanori Adachi, Tokyo Metropolitan University
17:00–17:30 Rusudan Kevkhishvili Kyoto University“On Decomposition of the Last Passage Time of Diﬀusions and its Financial
Application”
17:30–18:00

Wataru Nozawa
Fukuoka University“A Model of Asset Price Booms”

September 27 (Fri)
Session 4 Chair: Tai-Ho Wang, The City University of New York
13:00–13:45 Andrea Macrina
University College London“Transition Risk Mitigation: The CLoCo Bond”
13:45–14:15

Makoto Shimoshimizu Tokyo University of Science“Continuous-time optimal execution under a transient market impact model ina Markovian environment”

14:15–14:45

Tomohiro Koike
Kyoto University“Optimal timing of energy eﬃciency policies based on household utility: Usinga general equilibrium model for optimal stopping problems”

Session 5 Chair: Jie Yen Fan, Monash University
15:00–15:45 Kazutoshi Yamazaki
University of Queensland“Non-zero-sum optimal stopping game with continuous versus periodic exercise
opportunities”
15:45–16:15

Ryoichi Suzuki
Ritsumeikan University“Clark-Ocone-Haussmann type formulas for additive processes and theirapplication to ﬁnance”

16:15–16:45

Takaaki Shiotani
The University of Tokyo“Modeling lead-lag eﬀect using bivariate Neyman-Scott processes with gamma
kernels”

Session 6 Chair: Toshinao Yoshiba, Tokyo Metropolitan University
17:00–17:30 Benjamin Poignard
Osaka University“Factor multivariate stochastic volatility models of high dimension”
17:30–18:00

Kohta Takehara
Tokyo Metropolitan University“Strategic Interactions in Setting Up Decentralized Exchanges: Conﬂict ofInterest between Liquidity Providers and Platformers”

18:00–18:10

Closing address by Yukio Muromachi, Directer of Finance Program,
Graduate School of Management, Tokyo Metropolitan University

September 26, 13:00–13:45

Relative entropy-regularized robust optimal order
execution under transient impact
Tai-Ho Wang
The City University of New YorkIn this talk, we cast optimal liquidation under linear temporary and transient price impact as arelative entropy-regularized robust optimal control problem. The problem is formulated as tomaximize a reward-risk functional associated with the order execution agent’s proﬁt-and-loss of
trading and the execution risk taking into account market’s liquidity and uncertainty over a classof absolutely continuous strategies. The problem is made into an entropy-regularized stochastic
diﬀerential game and is solved by adopting the principle of dynamic programming, yielding thatthe value function of the diﬀerential game satisﬁes an entropy-regularized Hamilton-JacobiIsaacs (rHJI) equation. Under the assumption of aggregate exponential transient impact andGaussian prior, the rHJI equation reduces to a matrix Riccati diﬀerential equation. Further
imposing constancy of the corresponding coeﬃcients, the matrix Riccati diﬀerential equation
can be linearized, resulting in analytical expressions for optimal strategy and trajectory as wellas the posterior distribution of market activity. The talk is based on a joint work with Xue
Cheng and Meng Wang.

September 26, 13:45–14:15

High-Frequency Trading and Risk Sharing Capacity inMarket Making with Asymmetric Information
Kiichi Kitajima
Mitsubishi UFJ Trust Investment Technology InstituteWe examine how the impact of asymmetric information on market liquidity and informationaleﬃciency in a market where some of the market makers have high-frequency trading capabilities.
Our proposed market microstructure model consists of heterogeneous-speed market makers andliquidity traders, the latter bringing private information. We ﬁnd that the degree of information
asymmetry may or may not improve liquidity, depending on the market structure. We also
show that the increase in the number of high-frequency market makers basically improves themarket liquidity, but degrades the liquidity in some situations. Our theoretical results imply
that ﬁnancial authorities need to examine the eﬀect of high-frequency market making carefully,
especially if asymmetric information is signiﬁcant among traders. This study is a joint workwith Katsumasa Nishide (Waseda University).

September 26, 14:15–14:45

Randomized multi-factor approximation for stochastic
volterra equations with fractional kernel
Tomooki Yuasa
Tokyo Metropolitan University

This talk introduces a numerical simulation method for the stochastic volterra equation (SVE)with the fractional kernel. The SVE with the fractional kernel appears in various rough volatility
models, which have recently gained attention as a model for the price process of risk assets.
The SVE is non-Markovian and non-semimartingale because the fractional kernel has asingularity. This makes it diﬃcult to apply traditional methods used for stochastic diﬀerential
equations (SDEs) directly. To address this, Jaber and Euch (2019) developed a method toapproximate the SVE with a multi-factor SDE by representing the fractional kernel as the
Laplace (gamma) integral and approximating the integral with numerical integration. The
usual discrete-time approximation can be applied to the multi-factor SDE, allowing option
prices to be calculated numerically by the Monte Carlo method.
In this study, we employ the Monte Carlo method instead of numerical integration to approximate the fractional kernel (gamma integral). For instance, if we use a gamma-distributed
random variable in the Monte Carlo method, the error in the multi-factor approximation is
not ﬁnite. We present conditions and a construction method for the random variable usedin the Monte Carlo method that ensures a ﬁnite error in the multi-factor approximation, andshow that the random number can be generated by the inverse transform method. Althoughnumerical integration is generally considered more accurate than the Monte Carlo method forone-dimensional integrals such as the fractional kernel (gamma integral), our numerical experiments show that the accuracy of the both methods is comparable. The reason for thisis presumably that the Monte Carlo method is also used in the numerical calculation of option prices, which has the eﬀect of increasing the number of the Monte Carlo method used toapproximate the fractional kernel.
This work is conducted in collaboration with Takanori Adachi, Natsuno Sawamura, andKohta Takehara from Tokyo Metropolitan University.

September 26, 15:00–15:45

From mimicking to local Brownian motions
Jie Yen Fan
Monash University

Motivated by questions in ﬁnance, we are interested in constructing new processes from existingones while preserving the marginal distributions and the martingale property. We call thismimicking. This would enable us to develop alternative models for asset prices, with the hopeof improving upon the existing ones, while retaining the (European) option prices. In thistalk, I will give some results on mimicking and introduce local Brownian motions, which areprocesses that behave locally like a Brownian motion.

September 26, 15:45–16:15

Formulas for ”delta” of the options whose underlying
asset prices are given by aﬃne processes
Yuma Tamura
Ritsumeikan University

If (Xtx )t≥0 is an underlying asset price whose initial value is x, ∂x E[f (Xtx )] can be thought of asthe ”delta” of the option. This study focused on squared Bessel processes and aﬃne processes,
and we derived some formulas concerning ∂x E[f (Xtx )]. The results can be applied to the CIR
model.

September 26, 16:15–16:45

Large deviation principle for rough volatility models
Ryoji Takano
Osaka University

A rough volatility model is a stochastic volatility model for an asset price process with volatility
being rough, meaning that the Hölder regularity of the volatility path is less than half. In thistalk, we will focus on the asymptotic behavior of implied volatility for short maturity underthose models and show that the large deviation principle provides the asymptotic behavior of
implied volatility.

September 26, 17:00–17:30

On Decomposition of the Last Passage Time ofDiﬀusions and its Financial Application
Rusudan Kevkhishvili
Kyoto University

This talk is based on the joint work with Masahiko Egami: ”On Decomposition of the Last
Passage Time of Diﬀusions” (arXiv, 2024). First, we will discuss the role played by the lastpassage time of a diﬀusion in ﬁnancial applications. Then, for a regular transient diﬀusion, we
provide a new decomposition formula of its last passage time to a certain state α together with
its application. This is accomplished by transforming the original diﬀusion into two diﬀusions
using the occupation time of the area above and below α. Based on these two processes, bothhaving a reﬂecting boundary at α, we derive the decomposition formula of the Laplace transformof the last passage time explicitly in a simple form in terms of Green functions. This equation
also leads to the Green function’s decomposition formula. We demonstrate an application ofthese formulas to a diﬀusion with two-valued parameters.

September 26, 17:30–18:00

A Model of Asset Price Booms
Wataru Nozawa
Fukuoka University

Episodes indicate that asset price booms are often triggered by the introduction of new assets
or technologies coupled with expansionary monetary policy. We propose a model to explore
this phenomenon. In our model, traders hold diverse opinions on asset valuation, with only themore optimistic traders choosing to purchase the asset from producers. This selection leads toasset overpricing. Expansionary monetary policy reduces borrowing costs for traders, allowing
a greater number of optimistic traders to enter the market, which can further amplify the
overpricing under certain parameter conditions.

September 27, 13:00–13:45

Transition Risk Mitigation: The CLoCo Bond
Andrea Macrina
University College London

Adjustments to governmental climate transition policies and uncertainties linked to the ability for industry sectors and consumers to manufacture and purchase low carbon technologies,
respectively, have led to an increasing need to embed a richer framework for uncertainty inclimate transition outcomes. Such uncertainties create a number of ﬁnancial risks for ﬁrms,
their investors, the banking sector, and potentially sovereign risks. The need thus arises forthe development of a bespoke pricing setup and ﬁnancial instruments, which oﬀer a mechanism
to share climate transition risk. As an example, we propose the so-called climate-contingent
convertible (CLoCo) bond. This instrument enables ﬁrms to reduce the risk of default due
to adverse climate transition policies over the product’s lifetime. The proposed ﬁnancial innovation implies reduced risk of default for ﬁrms, thereby increasing the expected ﬁrm value,
but it also reduces the dependency of ﬁrm failures on the banking sector and potential bailout costs incurred by sovereign nations. Joint work with C. Cormack – SSRN working paper:https://dx.doi.org/10.2139/ssrn.4851975

September 27, 13:45–14:15

Continuous-time optimal execution under a transient
market impact model in a Markovian environment
Makoto Shimoshimizu
Tokyo University of Science

This paper examines a continuous-time optimal trade execution problem under a transient
market impact model. We also analyze the eﬀect of an exogenous random factor that aﬀects
the market price on the optimal trade execution strategy. Our execution problem is formulated as a continuous-time stochastic control problem over a ﬁnite horizon of maximizing the
expected utility from the ﬁnal wealth of a risk-averse large trader. By examining the HamiltonJacobi-Bellman (HJB) equation, we characterize the optimal trade execution strategy and its
associated optimal value function. The trade execution strategy becomes a time-dependentaﬃne function of state variables. Further, the time-dependent coeﬃcients could be derived
from a solution of a system of ordinary diﬀerential equations (ODEs) with terminal conditions,which is numerically tractable. In addition, we conduct simulation-based numerical experiments
and conﬁrm that the optimal execution strategy captures some features observed in ﬁnancial
markets.

September 27, 14:15–14:45

Optimal timing of energy eﬃciency policies based onhousehold utility: Using a general equilibrium model for
optimal stopping problems
Tomohiro Koike
Kyoto University

Policymakers are concerned with eﬀects of energy eﬃciency policies (EEPs) not only on environmental quality but also on household consumption. Thus, we study the optimal timing of
EEP implementation by considering household consumption and incorporating a general equilibrium model with an optimal stopping problem. This model is general in that energy prices
are governed by a stochastic process in a wide class of one-dimensional diﬀusion processes, andwe solve it by an analytical method. Moreover, we specify the energy price in an exponential
Ornstein-Uhlenbeck process and quantitatively analyze this model. Key results are as follows:(i) The additional household utility gained from EEPs is larger when energy prices are higher.
Thus, EEPs can mitigate the loss of household utility caused by high energy prices. (ii) An
increase in energy price volatility causes an increase in energy usage and output, but it has little
impact on the households’ utility of the economy. (iii) Increasing volatility and sustained priceshocks delay EEP implementation. (iv) The ability of EEPs to reduce energy consumption depends on the average level of energy prices and the energy intensity of production technology.
The baseline model of this study shows that the EEPs reduce energy consumption.

September 27, 15:00–15:45

Non-zero-sum optimal stopping game with continuous
versus periodic exercise opportunities
Kazutoshi Yamazaki
University of Queensland

We introduce a new non-zero-sum game of optimal stopping with asymmetric exercise opportunities. Given a stochastic process modelling the value of an asset, one player observes andcan act on the process continuously, while the other player can act on it only periodically at
independent Poisson arrival times. The ﬁrst one to stop receives a reward, diﬀerent for eachplayer, while the other one gets nothing. We study how each player balances the maximisationof gains against the maximisation of the likelihood of stopping before the opponent. In sucha setup, driven by a Lévy process with positive jumps, we not only prove the existence, butalso explicitly construct a Nash equilibrium with values of the game written in terms of thescale function. Numerical illustrations with put-option payoﬀs are also provided to study the
behaviour of the players’ strategies as well as the quantiﬁcation of the value of available exercise
opportunities. (Joint with Jose Luis Perez and Neofytos Rodosthenous)

September 27, 15:45–16:15

Clark-Ocone-Haussmann type formulas for additive
processes and their application to ﬁnance
Ryoichi Suzuki
Ritsumeikan University

This presentation investigates the development and application of Clark-Ocone-Haussmann(COH) type formulas for additive processes within the ﬁeld of mathematical ﬁnance, based oncollaborative research with M. Handa, N. Sakuma, and M. E. Mancino. COH formulas are fundamental in stochastic analysis, providing explicit martingale representations of random variables in terms of their Malliavin derivatives. Additionally, we explore Malliavin-Mancino-Taylor
type formulas, which extend the COH framework through high-order Malliavin derivatives, andexamine their applications in ﬁnance.

September 27, 16:15–16:45

Modeling lead-lag eﬀect using bivariate Neyman-Scottprocesses with gamma kernels
Takaaki Shiotani
The University of Tokyo

We propose noisy bivariate Neyman-Scott point processes with gamma kernels (NBNSP-G) tomodel the lead-lag relationships in high-frequency ﬁnancial data. The model tolerates noisesthat are not necessarily Poissonian, and the diverging gamma kernels represent fast responses
to new information in high-frequency trading. Our experiments suggest that NBNSP-G can
explain the correlation structure of executed orders of two stocks well. A composite-type quasilikelihood is employed to estimate the model’s parameters. However, when one tries to proveconsistency and asymptotic normality, NBNSP-G breaks the boundedness assumption on the
moment density functions commonly assumed in the literature. Therefore, we show consistency
and asymptotic normality under more relaxed conditions for bivariate point process models,
including NBNSP-G.

September 27, 17:00–17:30

Factor multivariate stochastic volatility models of highdimension
Benjamin Poignard
Osaka University

Building upon the pertinence of the factor decomposition to break the curse of dimensionality inherent to multivariate volatility processes, we develop a factor model-based multivariate
stochastic volatility (fMSV) framework that relies on two viewpoints: sparse approximate factor model and sparse factor loading matrix. We propose a two-stage estimation procedure forthe fMSV model: the ﬁrst stage obtains the estimators of the factor model, and the second
stage estimates the MSV part using the estimated common factor variables. We derive theasymptotic properties of the estimators. Simulated experiments and real data applications are
performed to assess the forecasting performances of the covariance matrices.

September 27, 17:30–18:00

Strategic Interactions in Setting Up Decentralized
Exchanges: Conﬂict of Interest between Liquidity
Providers and Platformers
Kohta Takehara
Tokyo Metropolitan University

Decentralized exchanges(DEXs) are a key concept in DeFi. Automated market makers, which
are algorithms that pool liquidity and make it available to users of the DEX at automaticallydetermined prices, are a common feature of such platforms. This study categorizes DEX players
into four groups: Platformers, Liquidity Providers, Arbitrageurs, and Traders. It then analyzes
how the structure of DEXs is aﬀected by the actions and optimizations of these players, whichis intuitively illustrated by several numerical examples. This is a joint work with Chiaki Hara,
Takanori Adachi and Tomooki Yuasa.