Option bounds for multinomial stock returns in Jump-Diffusion processes - a Monte Carlo simulation for a multi-jump process

This paper addresses the problem of option bounds computation under the assumption that the price of the underlying asset follows a jump-diffusion Merton process as formulated in Perrakis (1993) extending the number of the jumps from one jump up and one jump down with fixed sizes to a finite number of jumps with sizes drawn from the lognormal distribution. The objective of this paper is to create a Monte Carlo simulation for the estimation of the bounds with various numbers of jumps and periods to maturity.Monte Carlo simulation, Jump-Diffusion processes, multi-jump process

Convertible Bonds: Default Risk and Uncertain Volatility

Within a default intensity approach we discuss the optimal exercise of the callable and convertible bonds. Pricing bounds for convertible bonds are derived in an uncertain volatility model, i.e. when the volatility of the stock price process lies between two extreme values.Convertible bond, game option, uncertain volatility, interest rate risk

The Value of Waiting to Invest

This paper studies the optimal timing of investment in an irreversible project where the benefits from the project and the investment cost follow continuous-time stochastic processes. The optimal time to invest and an explicit formula for the value of the option to invest are derived. The rule "invest if benefits exceed costs" does not properly account for the option value of waiting.Simulations show that this option value can be significant, and that for surprisingly reasonable parameter values it may be optimal to wait until benefits are twice the investment cost. Finally, we perform comparative static analysis on the valuation formula and on the rule for when to invest.

An Uncertain Volatility Explanation for Delayed Calls of Convertible Bonds

Arbitrage-free price bounds for convertible bonds are obtained assuming a stochastic volatility process for the common stock that lies within a band but makes few other assumptions about volatility dynamics. Equity-linked hazard rates, stochastic interest rates and different assumptions about default and recovery behavior are accommodated within this approach. A non-linear multi-factor reduced-form equity-linked default model leads to a set of non-linear partial differential complementarity equations that are governed by the volatility path. Empirical results focus on call notice period effects, showing that uncertain volatility can capture the call premia so often observed in issuer’s call policies. Increasingly pessimistic values for the issuer’s substitution asset obtain as we introduce more uncertainty during the notice period. Volatility uncertainty is thus a useful mechanism to explain issuers delayed call policies.call notice period, call premium, convertible bond, delayed calls, equity-linked default, stochastic interest rates, volatility uncertainty