We develop a new approach for pricing European-style contingent claims written on the time
T spot price of an underlying asset whose volatility is stochastic. Like most of the stochastic …

Equity-linked products such as equity-indexed annuities (EIAs) provide their customers with
the greater of either the return linked to the underlying index or the minimum guaranteed …

The lookback feature in a quanto option refers to the payoff structure where the terminal
payoff of the quanto option depends on the realized extreme value of either the stock price …

Double barrier options have been traded for a long time in the markets and they are
embedded in a variety of popular structured products. However, in their standard form, they …

Suppose X is a diffusion process, possibly multivariate, and suppose that there are various
segments of the components of X that are missing. This happens, for example, if X is the …

Lévy processes can be used to model asset return's distributions. Monte Carlo methods
must frequently be used to value path dependent options in these models, but Monte Carlo …

The direct valuation procedure of performing discounted expectation to obtain the prices of
multi-state lookback options may lead to insurmountable complexity and numerical …

Pricing single asset American options is a hard problem in mathematical finance. There are
no closed form solutions available (apart from in the case of the perpetual option), so many …

We present importance sampling and acceptance–rejection simulation methods for one
dimensional diffusions. This effectively reduces the computation of many path functionals of …

It is shown how to obtain explicit formulae for a variety of popular path-dependent contracts
with complex payoffs involving joint distributions of several extrema. More specifically …