In Foreign Exchange Markets Compound options (options on options) are traded frequently. Instalment options generalize the concept of Compound options as they allow the holder to prolong a Vanilla Call or Put option by paying instalments of a discrete payment plan. We derive a closed-form solution to the value of such an option in the Black-Scholes model and prove that the limiting case of an I...

Many variable annuities provide money-back guarantees and market guarantees on invested principal. Embedded in some of these guarantees are stochastic maturity put options with adjustable strike prices. These variable annuities can be surrendered or lapsed at any time. The lapse option when exercised rationally represents an American style sell-back option that is exercised by the policyholder ...

A previous paper (West 2005) tackled the issue of calculating accurate uni-, biand trivariate normal probabilities. This has important applications in the pricing of multi-asset options, e.g. rainbow options. In this paper, we derive the Black–Scholes prices of several styles of (multi-asset) rainbow options using change-of-numeraire machinery. Hedging issues and deviations from the Black-Schol...

Put options are commonly used in the stock market to protect against the decline of the price of a stock below a specified price. On the other hand, finite difference approach is a well-known and well-resulted numerical scheme for financial differential equations. As such in this work, a new spatial discretization based on finite difference semi-discretization procedure with high order of accur...

This paper considers the American put option valuation in a jumpdiffusion model and relates this optimal-stopping problem to a parabolic integrodifferential free-boundary problem, with special attention to the behavior of the optimal-stopping boundary. We study the regularity of the American option value and obtain in particular a decomposition of the American put option price as the sum of its...