This paper proposes a generalized pricing formula and sensitivity analysis for sequential compound options (SCOs). Most compound options described in literatures, initiating by Geske [Geske, R., 1977. The Valuation of Corporate Liabilities as Compound Options. Journal of Finance and Quantitative Analysis, 12, 541–552; Geske, R., 1979. The Valuation of Compound Options. Journal of Financial Econ...

Abstract In recent years a number of authors pointed out significant stability and convergence problems while using Cox-Ross-Rubinstein binomial method to price and hedge barrier options. Different modifications were suggested to improve the convergence and stability of the binomial method. However, as this article shows, lattice approach in general has limited stability factor when applied to ...

This paper questions one of the fundamental assumptions made in options pricing: that the daily returns of a stock are independent and identically distributed (IID). We apply an estimation procedure to years of daily return data for all stocks in the French CAC-40 index. We find six stocks whose log returns are best modeled by a first-orderMarkov chain, not an IID sequence. We further propose t...

A new model on European options with uncertainty of both randomness and fuzziness in output is presented, by introducing fuzzy logic to the stochastic financial model. The randomness and fuzziness in the systems are evaluated by both probabilistic expectation and fuzzy expectation, taking account of seller s/buyer s subjective judgment. Prices of European call/put options with uncertainty are g...

The Pricing of Bermudan Options on Defaultable Bonds In this paper, we modify the Nelson and Ramaswamy (1990)-Ho, Stapleton and Subrahmanyam (1995) diffusion approximation. The modification allows the approximation of correlated lognormal diffusion processes. The general method is illustrated by pricing a Bermudan-style put option on the minimum of two asset prices. We then apply the method to ...

This paper will derive the Black-Scholes pricing model of a European option by calculating the expected value of the option. We will assume that the stock price is log-normally distributed and that the universe is riskneutral. Then, using Ito’s Lemma, we will justify the use of the risk-neutral rate in these initial calculations. Finally, we will prove put-call parity in order to price European...