BSM MODEL

Stochastic Differential Equations Pricing Derivative in Continuous-time- BSM Model

Stochastic Differential Equations Pricing Derivative in Continuous-time- BSM Model

This proposal will evaluate the he real estate derivatives market that allows participants to manage risk and return from exposure to property, without buying or selling directly the underlying asset. Such a market is growing very fast hence the need to rely on simple yet effective pricing models is very great. In order to take into account the real estate market sensitivity to the interest rate term structure in this will present a two-factor model where the real estate asset value and the spot rate dynamics are jointly modelled. The pricing problem for both European and American options will be then analyzed and since no closed-form solution can be found a bidimensional binomial lattice framework will be adopted. The model proposed will be able to fit the interest rate and volatility term structures.

The derivatives pricing problem roots lie in the seminal papers by Black and Scholes [1] and Merton [2] (hereafter BSM). They were the first to analytically solve the option pricing problem and for this achievement in 1997 were awarded the Nobel prize. This paper relies on the BSM risk-neutral valuation framework adapting it to the peculiarity of the real estate derivatives. In fact this class of contracts is characterized by a payoff dependent on an underlying real estate asset whose value depends on the interest rate dynamics. In particular in this paper the real estate asset value is represented by a geometric Brownian motion whereas the spot interest rate, which in the standard BSM framework is considered as a constant parameter, is properly modelled as a stochastic variable.

The proposal will present the two-factor pricing model in continuous time and derive the general valuation equation for any real estate derivative ...