We propose a stochastic model to develop a partial integro-differential equation (PIDE) for pricing and pricing expression for fixed type single Barrier options based on the Itô-Lévy calculus with the help of Mellin transform. The stock price is driven by a class of infinite activity Lévy...

Prices of financial options in a market with liquidity risk are shown to be weak solutions of a class of semilinear parabolic partial differential equations with nonnegative characteristic form. We prove the existence and uniqueness of such solutions, and then show the solutions correspond to...

We apply the Malliavin calculus to the stochastic string framework and obtain a Clark-Ocone-like formula. This result allows us to rewrite the hedging portfolio explicitly in terms of the Malliavin derivative of the discounted payoff. We illustrate this new result with two applications. Firstly,...

Due to the uncertainty in reality consists of randomness and fuzziness, we employ stochastic analysis and fuzzy set theory to explore the pricing of geometric Asian options. In the fuzzy stochastic world, the price of the underlying asset is assumed to follow a fuzzy stochastic process of which...

We present a one-factor local volatility model in discrete time to price and calibrate year-on-year and zero-coupon inflation options. This model provides an exact fit to year-on-year implied volatilities and to year-on-year forward convexity adjustments, for all strikes and maturities. It is...

We find explicit formulas for the moments of the time integral of an exponential Lévy process. We consider both the cases of unconditional moments and conditional on the Lévy process level at the endpoints of the time interval. We propose a new methodology for reconstructing the unknown...

This article establishes the Poisson optional stopping times (POST) method by Lange et al. (2020) as a near-universal method for solving liquidity-constrained American options, or, equivalently, penalised optimal-stopping problems. In this setup, the decision maker is permitted to “stop”,...

Uncertainty finance presents alternative models for derivative valuation relevant to markets willing to consider subjective information or expert criterium in their operation. This paper proposes a methodology based on experimental data for comparing the prices and the delta and vega risks for...

I examine a dataset of short-dated gasoline crack spread options traded on NYMEX using a two-asset version of Black (1976) model and find that the changes in implied correlations display economically significant variations not explained by changes in futures prices or changes in implied...

This paper contributes a generic probabilistic method to derive explicit exact probability densities for stochastic volatility models. Our method is based on a novel application of the exponential measure change in Palmowski & Rolski (2002). With this generic approach, we first derive explicit...