This paper provides two modified pricing PDEs for a general European option under liquidity risk, by which two modified hedges are derived. It is shown that the hedge errors of the two modified hedges approach zero as the trading time interval converges to zero inclusive of liquidity costs. An...

We discuss how implied volatilities for OTC traded Asian options can be computed by combining Monte Carlo techniques with the Newton method in order to solve nonlinear equations. The method relies on accurate and fast computation of the corresponding vegas of the option. In order to achieve this...

Geometric mean reversion plays a fundamental role in economic dynamic models. While it is known, at least since Merton (1975) [9], that the equilibrium distribution of geometric mean reversion is a Gamma distribution, an explicit expression for the non-equilibrium distribution has not been...

We discuss how implied volatilities for OTC traded Asian options can be computed by combining Monte Carlo techniques with the Newton method in order to solve nonlinear equations. The method relies on accurate and fast computation of the corresponding vegas of the option. In order to achieve this...

This paper derives an analytic expression for the distribution of the average volatility $\frac{1}{T-t} \int_t^T \sigma_s^2 ds$ in the stochastic volatility model of Hull and White. This result answers a longstanding question, posed by Hull and White (Journal of Finance 42, 1987), whether such...

We study the classical real option problem in which an agent faces the decision if and when to invest optimally into a project. The investment is assumed to be irreversible. This problem has been studied by Myers and Majd [18] for the case of a complete market, in which the risk can be perfectly...

We study the classical geometric mean reversion process which has been used to model commodity prices by various authors in Economics and Finance. We obtain certain regularity results which guarantee positivity and the existence of a stationary distribution. More important we derive an...

We consider a firm with assets-in-place and a growth option. There is a funding gap for the expansion investment, which is covered by entering into an equity-for-guarantee swap or fee-for-guarantee swap. We explicitly derive all contingent claim prices with the pricing and timing of the growth...

We study the impact of ambiguity on the pricing and timing of the option to invest. There is a funding gap to undertake the investment, which is covered by entering into an equity-for-guarantee swap (EGS). Our model predicts that the more ambiguity-averse the agents, the less the option value,...

We consider an entrepreneur who has no assets in place but possesses an option to invest in a project incurring a lump-sum investment cost, of which a fraction must be financed by entering into an equity-for-guarantee swap. The entrepreneur is exposed to macroeconomic risk as well as...