We review the continuous{time literature on the so{called direct approach to bond option pricing. Going back to Ball and Torous (1983), this approach models bond price processes directly (i.e. without reference to interest rates or state variable processes) and applies methods that Black and Scholes (1973) and Merton (1973) had originally developed for stock options. We describe the principal m...

Formulae for the distribution of the losses of a loan portfolio that are both realistic and simple enough to be implemented in a spreadsheet are hard to come by. The most prominent example is the Vasicek (1987) formula which is based upon a simplified version of the multivariate Merton (1974) model. Using an algorithm from the theory of Archimedean Copula functions, this paper gives some more l...

The Impact on Option Pricing of Specification Error in the Underlying Stock Price Returns Author(s): Robert C. Merton Source: The Journal of Finance, Vol. 31, No. 2, Papers and Proceedings of the Thirty-Fourth Annual Meeting of the American Finance Association Dallas, Texas December 28-30, 1975 (May, 1976), pp. 333-350 Published by: Blackwell Publishing for the American Finance Association Stab...

We analyse a general equilibrium model in which there is both adverse selection of and moral hazard by banks. The regulator has two tools at her disposal to combat these problems she can audit banks to learn their type prior to giving them a licence, and she can impose capital adequacy requirements. When the regulator has a strong reputation for screening she uses capital requirements to combat...

We present a closed-form ∆-hedging result for a large investor whose trades generate adverse market impact. Unlike in the complete-market case, the agent no longer finds it tenable to be perfectly hedged or even within a fixed distance away from being hedged. Instead, he may find himself arbitrarily mishedged and optimally trades towards the classical Black-Scholes ∆, with trading intensity pro...

Many scientists have told me how disappointing it is to have their research anticipated by other independent investigators. To have your ideas preempted in print just as you are about to publish is especially frustrating. A few studies suggest [hat anticipated research is an occupational hazard for the nraj”ori[rv of active researchers. Indeed, some investigators report being anticipated severa...

Central banks and supervisory authorities regularly conduct stress tests of banks. As losses accumulate in scenarios, banks’ equity position worsens, they must pay higher interest rates to retain funding. I explore how variations Merton-type models can be used measure bank risk, then examine the link between various risk measures funding costs. Finally, outline a method for incorporating cost i...

We study the Merton portfolio optimization problem in the presence of stochastic volatility using asymptotic approximations when the volatility process is characterized by its time scales of fluctuation. This approach is tractable because it treats the incomplete markets problem as a perturbation around the complete market constant volatility problem for the value function, which is well-unders...

In this note we value and hedge European options on assets paying discrete stochastic dividends. Our hedging strategy is based only on the underlying asset, risk-free bonds and dividend strips. Our simple strategy is easily seen to be compatible with early results based, among other things, on the existence of a dividend forward contract. Such contracts, however, are not traded in the market pl...

The fact that expected payo¤s on assets and call options are in...nite under most log-stable distributions led both Paul Samuelson (as quoted by Smith 1976) and Robert Merton (1976) to conjecture that assets and derivatives could not be reasonably priced under these distributions, despite their attractive feature as limiting distributions under the Generalized Central Limit Theorem. Carr and Wu...