Forecasting the Distribution of Option Returns

Stochastic volatility and jumps are viewed as arising from Brownian subordination given here by an independent purely discontinuous process and we inquire into the relation between the realized variance or quadratic variation of the process and the time change. The class of models considered encompasses a wide range of models employed in practical financial modeling. It is shown that in general the time change cannot be recovered from the composite process and we obtain its conditional distribution in a variety of cases. The implications of our results for working with stochastic volatility models in general is also described. We solve the recovery problem, i.e. the identification the conditional law for a variety of cases, the simplest solution being for the gamma time change when this conditional law is that of the first hitting time process of Brownian motion with drift attaining the level of the variation of the time changed process. We also introduce and solve in certain cases the problem of stochastic scaling. A stochastic scalar is a subordinator that recovers the law of a given subordinator when evaluated at an independent and time scaled copy of the given subordinator. These results are of importance in comparing price quality delivered by alternate exchanges.

This article investigates the relationship between initial margin requirements and stock return volatility. Volatility is measured using a GARCH in Mean model. We find no evidence of an empirical relationship between margin requirements and the volatility of the S&P 500 index portfolio's excess returns. Evidence from short-sale data, and model sensitivity analysis are presented which support the hypothesis of no margin-volatility relationship. The results are consistent with the intertemporal CAPM model of Merton (1973) with an aggregate relative risk aversion measure of 4.1. In addition, we find evidence of long-term memory in conditional return distributions' volatility.

Beyond Payoff Diagrams: How to Present Risk and Return Characteristics of Structured Products

Stochastic Local Volatility

The primary objective of this paper is to examine the market risk and liquidity risk management techniques and practices followed by the Indian scheduled commercial banks (SCB) consisting of public sector banks (PSBs) and private sector banks (PVSBs) for five years from 2016-17 to 2020-21. The other objective is to compare market and liquidity risk management practices between the public sector banks (PSBs) and private sector of banks (PVSBs). The other purpose of the study is to review the strategies adopted by the SCBs in risk management practices. To study the risk management practices, six largest banks each from PSBs and PVSBs are taken for sample study. This study finds that the SCBs are facing credit risk, market risk (Interest rate risk, foreign exchange risk, commodity price risk and equity price risk,) liquidity risk and operational risk. It also finds that the PSBs are better reporting and presenting their risk management practices in their annual reports than that of PVSBs in risk identification, risk assessment and risk analysis. The results indicate that there is no significant difference between the PVSBs and PSBs in the policies and practices of market risk and liquidity risk assessment, evaluation, monitoring risk controlling and risk taking. This paper will be relevant and value to those interested in research in the risk management banking industry. This is a descriptive research based on secondary data.

Stochastic Portfolio Theory Optimization and the Origin of Alternative Asset Allocation Strategies

This thesis presents our study on using the hybrid stochastic-local volatility model for option pricing. Many researchers have demonstrated that stochastic volatility models cannot capture the whole volatility surface accurately, although the model parameters have been calibrated to replicate the market implied volatility data for near at-the-money strikes. On the other hand, the local volatility model can reproduce the implied volatility surface, whereas it does not consider the stochastic behaviour of the volatility. To combine the advantages of stochastic volatility (SV) and local volatility (LV) models, a class of stochastic-local volatility (SLV) models has been developed. The SLV model contains a stochastic volatility component represented by a volatility process and a local volatility component represented by a so-called leverage function. The leverage function can be roughly seen as a ratio between local volatility and conditional expectation of stochastic volatility. The difficulty of implementing the SLV model lies in the calibration of the leverage function. In the thesis, we first review the fundamental theories of stochastic differential equations and the classic option pricing models, and study the behaviour of the volatility in the context of FX market. We then introduce the SLV model and illustrate our implementation of the calibration and pricing procedure. We apply the SLV model to exotic option pricing in the FX market and compare pricing results of the SLV model with pure local volatility and pure stochastic volatility models. Numerical results show that the SLV model can match the implied volatility surface very well as well as improve the pricing performance for barrier options. In addition, we further discuss some extensions of the SLV project, such as parallelization potential for accelerating option pricing and pricing techniques for window barrier options. Although the SLV model we use in the thesis is not entirely new, we contribute to the research in the following aspects: 1) we investigate the hybrid volatility modeling thoroughly from theoretical backgrounds to practical implementations; 2) we resolve some critical issues in implementing the SLV model such as developing a fast and stable numerical method to derive the leverage function; and 3) we build a robust calibration and pricing platform under the SLV model, which can be extended for practical uses.

This thesis presents our study on using the hybrid stochastic-local volatility model for option pricing. Many researchers have demonstrated that stochastic volatility models cannot capture the whole volatility surface accurately, although the model parameters have been calibrated to replicate the market implied volatility data for near at-the-money strikes. On the other hand, the local volatility model can reproduce the implied volatility surface, whereas it does not consider the stochastic behaviour of the volatility. To combine the advantages of stochastic volatility (SV) and local volatility (LV) models, a class of stochastic-local volatility (SLV) models has been developed. The SLV model contains a stochastic volatility component represented by a volatility process and a local volatility component represented by a so-called leverage function. The leverage function can be roughly seen as a ratio between local volatility and conditional expectation of stochastic volatility. The difficulty of implementing the SLV model lies in the calibration of the leverage function. In the thesis, we first review the fundamental theories of stochastic differential equations and the classic option pricing models, and study the behaviour of the volatility in the context of FX market. We then introduce the SLV model and illustrate our implementation of the calibration and pricing procedure. We apply the SLV model to exotic option pricing in the FX market and compare pricing results of the SLV model with pure local volatility and pure stochastic volatility models. Numerical results show that the SLV model can match the implied volatility surface very well as well as improve the pricing performance for barrier options. In addition, we further discuss some extensions of the SLV project, such as parallelization potential for accelerating option pricing and pricing techniques for window barrier options. Although the SLV model we use in the thesis is not entirely new, we contribute to the research in the following aspects: 1) we investigate the hybrid volatility modeling thoroughly from theoretical backgrounds to practical implementations; 2) we resolve some critical issues in implementing the SLV model such as developing a fast and stable numerical method to derive the leverage function; and 3) we build a robust calibration and pricing platform under the SLV model, which can be extended for practical uses.

Dynamic derivative strategies

Understanding Index Option Returns

Degree and structure of return dependence among commodities, energy stocks and international equity markets during the post-COVID-19 period

On Weak Predictor-Corrector Schemes for Jump-Diffusion Processes in Finance -- Moving Least Squares for Arbitrage-Free Price and Volatility Surfaces -- Solving Impulse Control Problems with Control Delays -- FIX: The Fear Index ? Measuring Market Fear -- American Option Pricing using Simulation and Regression: Numerical Convergence Results -- The COS Method for Pricing Options under Uncertain Volatility -- Fast Fourier Transform Option Pricing: Efficient Approximation Methods under Multi-Factor Stochastic Volatility and Jumps -- Pricing Credit Derivatives in a Wiener-Hopf Framework -- The Evaluation of Gas Swing Contracts with Regime Switching -- A Linear and Nonlinear Review of the Arbitrage-Free Parity Theory for the CDS and Bond Markets.

Portfolio Optimization with Ambiguous Correlation and Stochastic Volatilities

Qualified market risk management of asset and liability portfolios or trading activities is of key importance for banks and financial institutions. It is not only about quantitative measurement of the risks, but also about organizational and regulatory principles. Besides relatively simple market risk measures, we will define and explain various approaches to Value at Risk (VaR) and Conditional VaR estimation and backtesting. The two risk measures are used for day-to-day management as well as key regulatory capital concepts, or as tools of strategic risk management based on economic capital allocation. Market risk management, in particular in case of OTC derivatives, is also closely related to the counterparty credit risk management and measurement in terms of CVA (Credit Valuation Adjustment) that will be in detail discussed in the last section of this chapter.

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