Complex systems-whether natural or artificial-are characterized by dynamic feedback loops, nonlinear interactions, and sensitivity to external shocks, all of which shape long-term outcomes 1,2 . Climate, agricultural markets, and financial systems exemplify such complexity, where extreme events can trigger cascading effects across interconnected sectors [3][4][5] . Agriculture is a cornerstone of the Indian economy, supporting millions of livelihoods and contributing significantly to the country's GDP [6][7][8] . The relationship between climate and agriculture is one such complex system where changes in temperature, precipitation and humidity influence crop productivity, which in turn affects market prices, farmer incomes, and policy responses 9,10 . Few crops in particular, are susceptible to these variations due to their regional dependence and economic significance. Rice grown in Assam, serves as a staple food for much of its population, making its production crucial for the people. Soybean, primarily cultivated in Madhya Pradesh, plays a key role as an oilseed and protein source, with significant contributions to India's agricultural export market. Similarly, cotton, a vital cash crop in Gujarat, supports both domestic and international textile industries. However, shifts in weather events can heavily disrupt their production, straining farmer livelihoods, destabilizing supply chains, and causing broader market fluctuations. The unpredictability of climate patterns has made price volatility an increasing concern for farmers, policymakers, and investors alike [11][12][13] . To mitigate this risk and ensure food security, the government of India introduced the Minimum Support Price (MSP) system during the green revolution. The MSP functions as a government-backed price insurance scheme, guaranteeing a minimum price for specific crops to protect farmers from price crashes 14 . Under this system, public agencies purchase crops at the MSP if market prices fall below it, while farmers can sell at higher prices if available. However, despite its protective intent, the MSP system has limitations, including limited procurement, rising input costs, and the absence of a legal guarantee, leading to widespread protests in different states. An important economic perspective on MSP is its similarity to a european put option, where the it acts as the strike price. Unlike crop insurance schemes in developed economies, Indian farmers receive this protection without paying a premium, reducing incentives to engage with formal agricultural insurance or commodity derivative markets. This has contributed to the underdevelopment of agricultural derivatives in India, weakening the sector's financial resilience. Due to the increasing variations in climate patterns and their adverse effect on crop price volatility, it is essential to integrate climate data with financial models to assess future risks. Traditional econometric models often fail to capture the non-linear and asymmetric effects of extreme weather events on agricultural markets. To address this gap, our study employs the Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGARCH) model 15,16 to estimate conditional volatility in the log-returns of price for rice (Assam), soybean (Madhya Pradesh), and cotton (Gujarat). With estimated conditional volatility as the dependent variable and meteorological data as independent variables, we further employ the Seasonal Autoregressive Integrated Moving Average with Exogenous regressors (SARIMAX) model 17 to estimate conditional volatility. The predicted volatility is then used as an input into the Black-Scholes model [18][19][20] for put options to calculate the premium for MSP-linked crop insurance. By incorporating high-resolution climate reanalysis datasets from the Copernicus Climate Change Service, we analyze historical trends and future climate scenarios (e.g., SSP2.4.5 and SSP5.8.5) to assess potential risks. The novel aspect of our study is investigating a risk management strategy that the government might adopt to stabilize farmers' incomes and bolster financial sustainability. In this approach, the government could hedge its costs incurred from MSP by purchasing crop price insurance linked to it, with the MSP serving as the strike price of a put option. A dedicated crop insurance fund should be established, financed through public revenue, green bonds, and international development aid, to support MSP in a fiscally responsible manner. Under this mechanism, the government would bear the cost of MSP only when market prices drop below the threshold, with insurance covering excess costs. By integrating volatility forecasts into this system, insurance companies can accurately calculate the premiums for such crop insurance policies using models like Black-Scholes, ensuring that the risk is appropriately priced and shared between the government, insurance fund and farmers. Additionally, partnerships between the government, private insurers, and reinsurance firms could diversify risk and reduce the long-term burden on taxpayers 21 . This would help manage risks associated with extreme weather events while ensuring long-term fiscal sustainability. This risk-hedging strategy contributes to the development of sustainable agricultural finance in India by managing the uncertainties associated with climate variability, encouraging investment in agricultural innovation, and improving long-term resilience, thereby supporting broader goals of food security and economic stability in the face of an uncertain climate future [22][23][24][25][26] . This study examines the intricate relationship between climate variability, agricultural price volatility, and risk-hedging mechanisms, offering a comprehensive approach to stabilizing India's agricultural sector. By integrating econometric modelling, high-resolution climate data, and financial instruments, we propose an innovative policy framework where government-backed crop insurance complements MSP, ensuring long-term fiscal sustainability. Our findings contribute to the broader goal of enhancing agricultural resilience, securing farmer incomes, and strengthening India's food security in an era of increasing climate uncertainty. The Government of India's Directorate of Marketing and Inspection operates the AGMARKNET web portal, which plays a crucial role in disseminating agricultural market information, including arrivals and prices of various agricultural commodities across India. The portal collects data from local agricultural markets through a specially designed application called "Agmark," enabling farmers, traders, and researchers to access real-time market trends and insights. The website for accessing the corresponding data is: AGMARKNET 27 . We have taken monthly data from Madhya Pradesh, Assam and Gujarat, covering the period from Oct-2001 to Dec-2024. The districts were considered based on the data availability for this period. The MSP data was sourced from the commodities database of "The Centre for Monitoring Indian Economy"(CMIE) 28 website.
Figure 1 shows price and MSP time series, for soybean in Madhya Pradesh, rice in Assam, and cotton in Gujarat. Historical (1970-2015) and projected (2015-2100) under IPCC's climate trends for average daily surface mean temperature (Tav), monthly maximum temperature (Tmax), monthly minimum temperature (Tmin), and cumulative monthly precipitation (P) over the Indian states of Madhya Pradesh, Assam and Gujarat have been investigated using gridded climate data from the Coupled Model Intercomparison Project Phase 6 (CMIP6). According to the model, the data, which was derived from the Copernicus Climate Data Store (CDS), had spatial resolutions ranging from 0.70°to 3.75°(~77 km to 417 km at the equator) according to the different global circulation models (GCMs). To account for the uncertainties in future climate projections, four GCMs [see Table 1] were used 29 . Table 1. List of GCMs used in the present study. Two Shared Socioeconomic Pathways (SSPs) have been utilised for future climate projections: SSP5-8.5, which represents a high greenhouse gases emissions trajectory, and SSP2-4.5, which represents a moderate emissions scenario. SSP2-4.5 relies on the "middle-of-the-road" assumption that by 2100, the radiative forcing would have stabilised at 4.5 W/m 2 due to moderate population increase, technological advancements, and climate regulations, with an anticipated 2.1-3.5°C raise in global temperatures over pre-industrial levels. On the other hand, SSP5-8.5 is a fossil fuel-driven development pathway that will result in 3.2-5.4°C temperature increases by 2100 and radiative forcing of 8.5 W/m 2 due to its rapid economic expansion and lack of climate mitigation 30 . In order to perform an adequate temporal analysis of temperature and precipitation patterns, monthly values of Tmax, Tmin, Tav, and P were aggregated to assess seasonal and annual changes. To evaluate changes in these variables over time, statistical techniques such as linear regression, time series analysis, and Mann-Kendall trend tests were used to evaluate historical patterns from 1970 to 2015. Under the SSP2-4.5 and SSP5-8.5 scenarios, which reflect medium and high emissions pathways, respectively, anomalies in temperature and precipitation were computed in relation to the historical baseline (1970-2015) for future projections (2015-2100). Figure 2 shows the 12-month moving average of maximum temperature and precipitation trends in Madhya Pradesh, Assam and Gujarat. The red shaded region represents the 12-month moving average ±1 standard deviations of the historical maximum temperature data, while the dark blue and the dark green shaded regions represent the 12-month moving average ±1 standard deviations of the maximum temperature SSP2-4.5 and SSP5-8.5 projections. The blue shaded region represents the 12-month moving average and 95% confidence intervals of the historical precipitation data, while the pink and purple regions represent the 12-month moving average and 95% confidence intervals of the precipitation SSP2-4.5 and SSP5-8.5 projections. Suppose P = {p t |t = 0, 1, 2, • • • , T } is the vector of historical prices of agricultural commodities (soybean, rice or cotton). The log-return is defined as We model r t as mean stationary process with mean as E(r t ) = 0 and Var(r t ) = E(r 2 t ) = σ 2 t . r 2 t is an unbiased estimator of σ 2 t (see Figure 3). The Exponential Generalised Autoregressive Conditional Heteroskedasticity (EGARCH) model 15,16 captures the conditional volatility (σ 2 t ) dynamics of the log-returns (r t ). The EGARCH model is given by:

• ν represent the constant term. It sets the baseline level of the logarithm of the conditional variance, • η t denote the innovation (error) term from the mean equation, • κ i (for i = 1, . . . , p) be the coefficients for the effect of past absolute shocks. It quantifies how the size of past shocks influences current volatility, • δ j (for j = 1, . . . , o) capture the asymmetric impact of past shocks, allowing the model to treat positive and negative shocks differently, • φ k (for k = 1, . . . , q) model the persistence in volatility by incorporating the influence of past log conditional variances. • p, o, and q denote the number of lagged terms for the magnitude effect, the asymmetric effect, and the persistence effect, respectively. Figure 3 shows the conditional volatility estimates. Once the conditional volatility (σ t ) is estimated from the EGARCH model, it is considered as a dependent variable in a Seasonal AutoRegressive Integrated Moving Average with Exogenous Regressors (SARIMAX) model 17 using meteorological variables as independent variables 10 . The SARIMAX model is an extension of the ARIMA model by incorporating seasonal and exogenous components, which makes the model suitable for agricultural price analysis. The SARIMAX model is written as:

where:

• A P (L s ): Seasonal AR operator of order P:

• a p (L): Non-seasonal AR operator of order p:

• m: Order of non-seasonal differencing. • M: Order of seasonal differencing. • s: Seasonal period (e.g., s = 12 for monthly data with annual seasonality). • b q (L): Non-seasonal MA operator of order q: b q

• ε t : Error term. • z t : Vector of exogenous regressors (e.g., tasmax for maximum temperature and pr for precipitation). • γ: Coefficient vector for the exogenous regressors. The fitted SARIMAX model is used to predict the conditional volatility ( σt ) and construct 68% prediction intervals:

as shown in Figure 4. One could directly incorporate exogenous climate variables into the variance equation of the EGARCH model. However, this method works best for short-and medium-term forecasting. On the other hand, the SARIMAX model is well-suited for long-term forecasting. Hence, we have adopted a two-step approach to fully utilise the SARIMAX model's potential for long-term volatility risk forecasting using meteorological predictions derived from Global Climate Models (GCM) as exogenous variables. We first fit the EGARCH model using the log-returns (r t ) to estimate the conditional volatility. Next, the SARIMAX model uses external variables (x t ) such as maximum temperature and precipitation to predict the estimated conditional volatility.
This two-step approach combines financial time series modelling with meteorological data, providing a reliable framework for forecasting volatility across various time horizons and different climate scenarios. In this study, MSP is conceptualized as a European put option, where the government guarantees a minimum price for agricultural produce, shielding farmers from market downturns. This analogy allows us to apply the Black-Scholes model [18][19][20] , providing a structured approach to estimating the premium of a crop insurance scheme designed to hedge against the financial burden of MSP. The price of a corresponding put option based on put-call parity is:

where:

Here, P is the put option price, S 0 is the current asset price (spot price of the crop), K is the strike price (MSP), T is time to maturity (duration of MSP policy), r is the risk free interest rate, σ is the volatility (predicted using SARIMAX) and Φ(.) is the cumulative distribution function of the standard normal distribution. The premium is calculated from the SARIMAX volatility estimates and its trend-line is plotted in Fig 5. This section presents and interprets the key findings of our analysis as shown in figures 1-5. The crop price and MSP time series as given in figure 1 illustrates the relationship between them for soybean in Madhya Pradesh, rice in Assam and cotton in Gujarat. In the case Assam (rice), the majority of paddy farmers are smallholders with limited market influence. As a result, the MSP remains significantly lower than the prevailing market price, reflecting the farmers' weaker bargaining power and the predominance of local procurement dynamics. Conversely, in Gujarat (cotton) and Madhya Pradesh (soybean), the presence of well-organized farmer unions has played a crucial role in ensuring that MSP remains closer to or even hovers around the market price. Figure 2 showcases the historical maximum temperature and precipitation trends in Madhya Pradesh, Assam, and Gujarat, with their future projections that increasingly diverge under two climate scenarios: SSP2-4.5 (moderate emissions) and SSP5-8.5 (high emissions). Figure 3 illustrates the conditional volatility estimates for soybean, rice and cotton modelled using EGARCH. Notably, rice prices exhibit relatively lower volatility compared to soybean and cotton except for the period of 2011-12 when prices increased erratically 31 . Figure 4 shows the conditional volatility estimates of the SARIMAX model when maximum temperature and precipitation are taken as exogenous variables. The volatility prediction for rice in Assam is lower, relative to soybean and cotton. Figure 5 portrays the smoothed crop insurance premiums under both scenarios for all three crops. The premiums of the 2 scenarios diverge after 2060 for soybean, 2080 for rice and 2030 for cotton. Tackling the challenges of MSP and Crop Insurance India's Minimum Support Price (MSP) system plays a crucial role in stabilizing farmers' incomes by guaranteeing a minimum price for certain crops. However, this policy has an unintended drawback: it reduces the incentive for farmers to purchase crop insurance. Since they are assured a baseline price, many see additional coverage as unnecessary, making them less likely to use private risk mitigation tools. While MSP has effectively supported farmers in the past, increasing agricultural market volatility, largely driven by climate change, makes it difficult for the government to sustain this financial burden alone. If MSP continues to serve as the primary risk management tool without complementary mechanisms, it could place immense pressure on public resources, potentially endangering long-term food security. One viable approach to easing this burden is for the government to use crop insurance as a financial safeguard. With climate variability increasing the costs of maintaining MSP, an insurance-backed strategy could help offset risks associated with the program. Without a structured risk-sharing model, the growing expense of MSP could become unsustainable, straining both state and central budgets. For instance, if annual MSP expenditure currently stands at INR 9 million, the government could set a legal cap at INR 10 million. Any costs exceeding this limit could be covered by an insurance policy, ensuring that sudden price swings do not destabilize public finances. By adopting this forward-thinking approach, policymakers could continue supporting farmers while mitigating financial risks in an increasingly unpredictable agricultural landscape. The government should take a more active role in managing agricultural price fluctuations. The current system disincentivizes insurance adoption because farmers are already assured of a minimum price. Instead, by purchasing large-scale crop insurance policies, the government could shield itself from extreme market volatility while ensuring the long-term sustainability of MSP. This strategy would also lessen dependence on taxpayer funds, as insurance mechanisms could absorb excess costs beyond a predefined threshold. By shifting financial risks to insurers, the government could maintain agricultural stability while reducing budgetary strain. Well-designed insurance policies could cover both price differences between market rates and MSP as well as weather-related losses. This would create a more robust and fiscally responsible risk management system, ensuring that MSP remains viable even as climate uncertainties grow. To make this model financially sustainable, the government could establish a dedicated crop insurance fund, sourcing capital from public revenues, green bonds, and international development assistance. Collaborating with private insurers and global reinsurance companies would further distribute risk efficiently, reducing the direct financial burden on the government. A comprehensive risk-sharing framework would help stabilize MSP-related expenditures while strengthening India's agricultural resilience. By assuming responsibility for crop insurance at a national level, the government could better manage long-term agricultural risks. Large-scale insurance purchases would allow for predictable public spending while still guaranteeing fair prices for farmers. Additionally, this strategy would enhance climate risk mitigation efforts, making Indian agriculture more adaptive to unpredictable environmental changes. In summary, the impact of climate variability on agricultural price fluctuations was examined, and a data-driven method for managing financial risks was introduced. Traditional models often ignore meteorological factors, reducing their accuracy.