Andrea Gheno

A model for pricing real estate derivatives with stochastic interest rates

The real estate derivatives market 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 paper is presented a two-factor model where the real estate asset value and the spot rate dynamics are jointly modeled. The pricing problem for both European and American options is then analyzed and since no closed-form solution can be found a bidimensional binomial lattice framework is adopted. The model proposed is able to fit the interest rate and volatility term structures.

Chapman-Kolmogorov lattice method for derivatives pricing

In this paper a novel, fast and accurate derivatives pricing method based on the application of the Chapman-Kolmogorov equation is introduced. It has an intuitive lattice representation and is able to price a wide range of derivatives. Comparisons with some advanced exotic options pricing techniques are also provided in order to confirm the efficiency of the method proposed.

Equity and Debt Valuation with Default Risk: a Discrete Structural Model

Structural models’ main source of uncertainty is the stochastic evolution of the firms asset value. These models are commonly used to value corporate debt at the issue and hence to determine its yield given the amortization plan. This paper proposes two discrete models to value securities issued by a firm which can default before the maturity of its debt either for exogenous or endogenous causes. In either case the equity value is set as the price of a knock-out call option with a discrete monitoring barrier. The first model considers a debt refundable through the payment of known endowments and takes into account that the firm defaults as it fails to meet a promised payment. In the second model the firms debt is made of a single issue of zero coupon bonds and includes the possibility that the firm defaults prior to the maturity of the debt if its asset value falls below a time dependent barrier. The particular evolution of the asset value, which shows discontinuity in the drift and diffusion coefficient, prevents the use of closed form solutions for options with a discrete monitoring barrier. The evaluation of the option is performed through non-recombining binomial trees.

Pricing and Applications of Digital Installment Options

For its theoretical interest and strong impact on financial markets, option valuation is considered one of the cornerstones of contemporary mathematical finance. This paper specifically studies the valuation of exotic options with digital payoff and flexible payment plan. By means of the Incomplete Fourier Transform, the pricing problem is solved in order to find integral representations of the upfront price for European call and put options. Several applications in the areas of corporate finance, insurance, and real options are discussed. Finally, a new type of digital derivative named supercash option is introduced and some payment schemes are also presented.