We introduce a new stochastic volatility model that includes, as special instances, the Heston (1993) and the 3/2 model of Heston (1997) and Platen (1997). Our model exhibits important features: first, instantaneous volatility can be uniformly bounded away from zero, and second, our model is...

We construct a binomial model for a guaranteed minimum withdrawal benefit (GMWB) rider to a variable annuity (VA) under optimal policyholder behaviour. The binomial model results in explicitly formulated perfect hedging strategies funded using only periodic fee income. We consider the separate...

Funding Valuation Adjustment (FVA) has been introduced as the CVA and DVA after the default of Lehman Brother. After the subprime crisis, the basis spread was not negligible anymore, credit and liquidity risk became the first concern. In addition, regulators put in place reforms, which associate...

After Lehman default and the Euro Crisis (crisis which started mid-2007), the industry started to consider the funding risk as a major risk. The practitioners began to charge for their funding cost. In this stressed context, the FVA has been the subject of intense debate, even its definition is...

We give a method based on convex programming to calculate the optimal super-replicating and sub-replicating prices and corresponding hedging portfolios of a financial derivative in terms of other financial derivatives in a discrete-time setting. Our method produces a model that matches the...

A selection of Fourier transform methodologies for option pricing is presented. The focus is aimed at the cosine method which is endowed with attractive properties. The methodologies are applied to a particularly selected pricing problem and also are compared against closed-form formulas if...

Guarantees embedded variable annuity contracts exhibit option-like payoff features and the pricing of such instruments naturally leads to risk neutral valuation techniques. This paper considers the pricing of two types of guarantees; namely, the Guaranteed Minimum Maturity Benefit and the...

We consider counterparty credit risk in the interest rate swap (IRS) contracts in the presence of an adverse dependence between the default time and interest rates, so-called wrong-way risk. The IRS credit valuation adjustment (CVA) semi-analytical formula based on Gaussian copula assumption,...

We discuss a competitive alternative to stochastic local volatility models, namely the Collocating Volatility (CV) model, introduced in Grzelak (2016). The CV model consists of two elements, a 'kernel process' that can be efficiently evaluated and a local volatility function. The latter, based...

We develop a new high-performance spectral collocation method for the computation of American put and call option prices. The proposed algorithm involves a carefully posed Jacobi-Newton iteration for the optimal exercise boundary, aided by Gauss-Legendre quadrature and Chebyshev polynomial...