Along with the well-known “call-put parity” relation, that makes it possible to express the rational price of a put option in terms of the rational price of a call option, we introduce a “call-put duality” relation. This new concept offers a simple explanation of the relationship between the rational price of a put option and a call option, not only for options of the European type, but also fo...

In this paper, we present an implicit finite difference method for the numerical solution of Black–Scholes model American put options without dividend payments. We combine proposed by using a front-fixing approach where option price and early exercise boundary are computed simultaneously. study consistency prove stability fixing values free its first derivative. improve accuracy via mesh refine...

A make-your-mind-up option is an American derivative with delivery lags. We show that its put can be decomposed as a European and new type of American-style derivative. The latter for which the investor receives Greek Theta corresponding running payoff, decides optimal stopping time to terminate contract. Based on this decomposition using free boundary techniques, we associated exercise exists ...

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...

Abstract Elementary proofs of classical theorems on pricing perpetual call and put options in the standard Black-Scholes model are given. The method presented does not rely on stochastic calculus and is also applied to give prices and optimal stopping rules for perpetual call options when the stock is driven by a Lévy process with no positive jumps, and for perpetual put options for stocks driv...

In this paper, we investigate the generalization of the Call-Put duality equality obtained in [1] for perpetual American options when the Call-Put payoff (y − x)+ is replaced by φ(x, y). It turns out that the duality still holds under monotonicity and concavity assumptions on φ. The specific analytical form of the Call-Put payoff only makes calculations easier but is not crucial unlike in the d...