Related papers: Option Pricing, Historical Volatility and Tail Ris…
We study convexity and monotonicity properties of option prices in a model with jumps using the fact that these prices satisfy certain parabolic integro-differential equations. Conditions are provided under which preservation of convexity…
The fundamental theorem behind financial markets is that stock prices are intrinsically complex and stochastic. One of the complexities is the volatility associated with stock prices. Volatility is a tendency for prices to change…
Consider an insurance company exposed to a stochastic economic environment that contains two kinds of risk. The first kind is the insurance risk caused by traditional insurance claims, and the second kind is the financial risk resulting…
Under a generalized skew normal distribution we consider the problem of European option pricing. Existence of the martingale measure is proved. An explicit expression for a given European option price is presented in terms of the cumulative…
Estimating and controlling large risks has become one of the main concern of financial institutions. This requires the development of adequate statistical models and theoretical tools (which go beyond the traditionnal theories based on…
We consider arbitrage free valuation of European options in Black-Scholes and Merton markets, where the general structure of the market is known, however the specific parameters are not known. In order to reflect this subjective uncertainty…
Generating realistic synthetic option prices requires implied volatility as an input, yet implied volatility is itself derived from observed option prices, creating a circular dependency that limits synthetic data for machine-learning and…
In this chapter, we consider volatility swap, variance swap and VIX future pricing under different stochastic volatility models and jump diffusion models which are commonly used in financial market. We use convexity correction approximation…
We introduce a price impact model which accounts for finite market depth, tightness and resilience. Its coupled bid- and ask-price dynamics induce convex liquidity costs. We provide existence of an optimal solution to the classical problem…
Accurately characterizing the implied volatility curves is a central challenge in option pricing and risk management. The classical SABR model by Hagan et al. has been widely adopted in practice due to its well-defined stochastic volatility…
We propose a method to bound the expectation of the supremum of the price process in stochastic volatility models. It can be applied, for example, to the rough Bergomi model, avoiding the need to discuss finiteness of higher moments. Our…
This paper quantifies the effects of equity tail risk on the US government bond market. We estimate equity tail risk with option-implied stock market volatility that stems from large negative price jumps, and we assess its value in…
In a stochastic volatility framework, we find a general pricing equation for the class of payoffs depending on the terminal value of a market asset and its final quadratic variation. This allows a pricing tool for European-style claims…
In this paper we study short-time behavior of the at-the-money implied volatility for Inverse European options with fixed strike price. The asset price is assumed to follow a general stochastic volatility process. Using techniques of the…
The vast majority of works on option pricing operate on the assumption of risk neutral valuation, and consequently focus on the expected value of option returns, and do not consider risk parameters, such as variance. We show that it is…
This paper enhances the pricing of derivatives as well as optimal control problems to a level comprising risk. We employ nested risk measures to quantify risk, investigate the limiting behavior of nested risk measures within the classical…
The aim of this paper is to present a simple stochastic model that accounts for the effects of a long-memory in volatility on option pricing. The starting point is the stochastic Black-Scholes equation involving volatility with long-range…
We use a continuous version of the standard deviation premium principle for pricing in incomplete equity markets by assuming that the investor issuing an unhedgeable derivative security requires compensation for this risk in the form of a…
In commodity and energy markets swing options allow the buyer to hedge against futures price fluctuations and to select its preferred delivery strategy within daily or periodic constraints, possibly fixed by observing quoted futures…
This paper focuses on the pricing of continuous geometric Asian options (GAOs) under a multifactor stochastic volatility model. The model considers fast and slow mean reverting factors of volatility, where slow volatility factor is…