In this dissertation we price European and American vanilla and barrier options assuming that the underlying follows the variance gamma process. We solve numerically the problem implementing a finite difference algorithm and we present numerical experiments on the option pricing. This...

Banks and other financial institutions raise hybrid capital as part of their risk capital. Hybrid capital has no maturity, but, similarily to most corporate debt, includes an embedded issuer's call option. To obtain acceptance as risk capital, the first possible exercise date of the embedded...

The first part of this document is dedicated to the pricing of undiscounted Vanilla Options: we compute the price and sensitivities of Calls and Puts, and highlight the different FX Delta conventions. The most important application of specific FX market conventions (and particularly Deltas...

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,...

The Accardi-Boukas quantum Black-Scholes framework, provides a means by which one can apply the Hudson-Parthasarathy quantum stochastic calculus to problems in finance. Solutions to these equations can be modelled using nonlocal diffusion processes, via a Kramers-Moyal expansion, and this...

In this paper, we propose a general framework for the valuation of options in stochas-tic local volatility (SLV) models with a general correlation structure, which includes the Stochastic Alpha Beta Rho (SABR) model and the quadratic SLV model as special cases. Standard stochastic volatility...

Under the recent negative interest rate situation, the Bachelier model has been attracting attention and adopted for evaluating the price of interest rate options. In this paper, we will derive an option pricing formula based on the Bachelier model and compare it with the prior researches. We...

The standard shifted lognormal model, defined by just two parameters, provides a remarkably good fit to the market implied volatilities of VIX options.Inspired by an analytic approximation derived by Lee and Wang, we propose a simple, intuitive extension that provides better empirical fits while...

This paper addresses several theoretical and practical issues in option pricing and implied volatility calibration in a fractional Black-Scholes market. In particular, we discuss how the fractional Black-Scholes model admits a non-constant implied volatility term structure when the Hurst...

The “practitioner Black-Scholes delta” for hedging options is a delta calculated from the Black-Scholes-Merton model (or one of its extensions) with the volatility parameter set equal to the implied volatility. As has been pointed out by a number of researchers, this delta does not minimize...