We study the detailed convergence of the binomial tree scheme. It is known that the scheme is first order. We find the exact constants, and show it is possible to modify Richardson extrapolation to get a method of order three-halves. We see that the delta, used in hedging, converges at the same rate. We analyze this by first embedding the tree scheme in the Black-Scholes diffusion model by mean...

In this work, we present a model to value capacity investment decisions based on real options. In the problem considered we incorporate partial reversibility by letting the firm reverse its capital investment at a cost, both fully or partially. The standard RO approach considers the stochastic variable to be normally distributed and then approximated by a binomial distribution, resulting in a b...

We propose using a real options framework to quantify the financial value of cross training. We model the investment decision in cross training as a series of European call options with the same exercise price but with different maturity dates. We use the Black-Scholes formula and the binomial tree approach to find the value of having the option to cross train. A case study shows the applicatio...

Modeling a nonlinear pay o¤ generating instrument is a challenging work. The models that are commonly used for pricing derivative might divided into two main classes; analytical and iterative models. This paper compares the Black-Scholes and binomial tree models.

Stochastic differential equations and the Black-Scholes PDE. We derived the BlackScholes formula by using arbitrage (risk-neutral) valuation in a discrete-time, binomial tree setting, then passing to a continuum limit. This section explores an alternative, continuoustime approach via the Ito calculus and the Black-Scholes differential equation. This material is very standard; I like Wilmott-How...

In the context of an asset paying affine-type discrete dividends, we present closed analytical approximations for the pricing of European vanilla options in the Black-Scholes model with time-dependent parameters. They are obtained using a stochastic Taylor expansion around a shifted lognormal proxy model. The final formulae are respectively first, second and third order approximations w.r.t. th...

In this paper we introduce and study random Cox-Ross-Rubinstein (CRR) model. The CRR model is a natural bridge, overture to continuous models for which it is possible to derive the Black Scholes option pricing formula. An attractive property of CRR model is that the binomial tree for geometric Brownian motion is consistent with the standard Black-Scholes formula for European options in that no ...