We develop a simulation algorithm for estimating the prices of American-style securities, i.e., securities with opportunities for early exercise. Our algorithm provides both point estimates and error bounds for the true security price. It generates two estimates, one biased high and one biased low, both asymptotically unbiased and converging to the true price. Combining the two estimators yields a confidence interval for the true price.
The payoff of a barrier option depends on whether or not a specified asset price, index, or rate reaches a specified level during the life of the option. Most models for pricing barrier options assume continuous monitoring of the barrier; under this assumption, the option can often be priced in closed form. Many (if not most) real contracts with barrier provisions specify discrete monitoring instants; there are essentially no formulas for pricing these options, and even numerical pricing is difficult.
In this paper we provide valuation formulas for several types of American options on two or more assets. Our contribution is twofold. First, we characterize the optimal exercise regions and provide valuation formulas for a number of American option contracts on multiple underlying assets with convex payoff functions. Examples include options on the maximum of two assets, dual strike options, spread options, exchange options, options on the product and powers of the product, and options on the arithmetic average of two assets.
We develop bounds and approximations for setting base-stock levels in production-inventory systems with limited production capacity. Our approximations become exact as inventories become critical, meaning either that the target service level is very high or the backorder penalty is very large. Our bounds apply even without this requirement. We consider both single-stage and multi-stage systems.
A methodology to price American options with finitely many exercise opportunities simulates the evolution of underlying assets via random trees that branch at each of the possible early exercise dates. From these trees, two consistent price estimates are obtained, one biased high and one biased low. These two estimates can be combined to provide a valid, though conservative confidence interval for the option price.
As the only practical way to deal with most path-dependent instruments, Monte Carlo estimation is now one of the workhorses of modern derivatives valuation. It has the advantage of being relatively easy to implement in its basic form, and, given enough computer resources, it will converge asymptotically to the correct answer. Yet, once these general principles are acknowledged, one faces the fact that many problems have such high dimension that the basic Monte Carlo technique can require an enormous number of simulations before convergence to a reasonably accurate answer is achieved.
We use when-issued transactions data to assess the Treasury's current experiment with uniform auctions. When-issued volume is higher under uniform as compared to discriminatory auctions, suggesting a higher information release, which should reduce pre-auction uncertainty and the winner's curse. Under uniform auctions, when-issued volatility falls after the auction and again after the outcome announcement. The pattern is the opposite for discriminatory auctions. This is further evidence that uniform auctions increase pre-auction information and lower the short squeeze.
We consider the problem of precise estimation of service-level measures in multistage production-inventory systems when the system is managed for high levels of service. Precisely because the service level is high, stockouts, large backorders, and unfilled demands are rare and thus difficult to estimate by straightfoward simulation. We propose and analyze alternative estimators, based on changing the demand distribution to make these rare events less rare.
We develop a simple approximation for multistage production-inventory systems with limited production capacity and variable demands. Each production stage follows a base-stock policy for echelon inventory, constrained by production capacity and the availability of upstream inventory. Our objective is to find base-stock levels that approximately minimize holding and backorder costs. The key step in our procedure approximates the distribution of echelon inventory by a sum of exponentials; the parameters of the exponentials are chosen to match asymptotically exact expressions.