We present an asymptotic solution for call options on zero-coupon bonds, assuming a stochastic process the price of bond, rather than interest rates in general. The bond incorporates dampening return volatility based maturity bond. derive PDE similar way to Black and Scholes. Using perturbation approach, we value option. result is interesting, as leading order terms are equivalent Black–Scholes...

This paper presents a new numerical method for pricing American call options when the volatility of the price of the underlying stock is stochastic. By exploiting a log-linear relationship of the optimal exercise boundary with respect to volatility changes, we derive an integral representation of an American call price and the early exercise premium which holds under stochastic volatility. This...

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...