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 new binomial approximation to the Black–Scholes model is introduced. It is shown that for digital options and vanilla European call and put options that a complete asymptotic expansion of the error in powers of n−1 exists. This is the first binomial tree for which such an asymptotic expansion has been shown to exist.

We reconsider the valuation of barrier options by means of binomial trees from a “forward looking” prospective rather than the more conventional “backward induction” one used by standard approaches. This reformulation allows us to write closed-form expressions for the value of European and American put barrier-options on a non-dividend-paying stock.

American put options with the regime-switching model is a system of coupled free boundary problems. In this study, we present an accurate finite difference method Hermite interpolation for solving system. To end, first employ logarithmic transformation to map each regime fixed interval and then eliminate first-order derivatives in transformed by taking obtain partial differential equations whic...

This paper is devoted to the derivation of some regularity properties of pricing functions for American options and to the discussion of numerical methods, based on the Bensoussan-Lions methods of varia-tional inequalities. In particular, we provide a complete justiication of the so-called Brennan-Schwartz algorithm for the valuation of Ameri-can put options.

We prove that the perpetual American put option price of level dependent volatility model with compound Poisson jumps is convex and is the classical solution of its associated quasi-variational inequality, that it is C except at the stopping boundary and that it is C everywhere (i.e. the smooth pasting condition always holds).

We study a free boundary problem arising from American put options. In particular we prove existence and uniqueness for this problem and we derive, and prove rigorously, high order asymptotic expansions for the early exercise boundary near expiry. We provide four approximations for the boundary: one is explicit and is valid near expiry (weeks); two others are implicit involving inverse function...

Many authors have argued, for good reasons, that in a range of applications the lens put-put law is too strong. On the other hand, the present authors have shown that very well behaved lenses, which do satisfy the put-put law by definition, are algebras for a certain monad, and that this viewpoint admits fruitful generalisations of the lens concept to a variety of base categories. In the algebr...