Financial Engineering

Abstract: In many of the numerical methods for pricing American options based on the dynamic programming approach, the most computationally intensive part can be formulated as the summation of Gaussians. Though this operation usually requires O(NN') work when there are N' summations to compute and the number of terms appearing in each summation is N, we can reduce the amount of work to O(N+N') by using a technique called the fast Gauss transform.

Motivated by the problem of efficient estimation of expected cumulative rewards or cashflows, this paper proposes and analyzes a variance reduction technique for estimating the expectation of the sum of sequentially simulated random variables. In some applications, simulation effort is of greater value when applied to early time steps rather than shared equally among all time steps; this occurs, for example, when discounting renders immediate rewards or cashflows more important than those in the future. This suggests that deliberately stopping some paths early may improve efficiency.

In this paper, we develop an approach for filtering state variables in the setting of continuous-time jump-diffusion models. Our method computes the filtering distribution of latent state variables conditional only on discretely observed observations in a manner consistent with the underlying continuous-time process. The algorithm is a combination of particle filtering methods and the "filling-in-the-missing-data" estimators which have recently become popular. We provide simulation evidence to verify that our method provides accurate inference.

This paper develops efficient methods for computing portfolio value-at-risk (VAR) when the underlying risk factors have a heavy-tailed distribution. In modeling heavy tails, we focus on multivariate t distributions and some extensions thereof. We develop two methods for VAR calculation that exploit a quadratic approximation to the portfolio loss, such as the delta-gamma approximation. In the first method, we derive the characteristic function of the quadratic approximation and then use numerical transform inversion to approximate the portfolio loss distribution.

This paper studies the economic benefits of return predictability by analyzing the impact of market and volatility timing on the performance of optimal portfolio rules. Using a model with time-varying expected returns and volatility, we form optimal portfolios sequentially and generate out-of-sample portfolio returns. We are careful to account for estimation risk and parameter learning.

We analyze a unique data set on multiunit auctions, which contains the actual demand schedules of the bidders as well as the auction awards in over 400 Swedish Treasury auctions. First, we document that bidders vary their prices, bid dispersion, and the quantity demanded in response to increased uncertainty at the time of bidding. Second, we find that bid shading can be explained by a winner's curse driven model in which each bidder submits only one bid, despite the fact that the bidders in our data set use much richer bidding strategies.

Minton, Schrand and Walther (2002) (MSW) investigate whether cash flow (earnings) volatility helps predict subsequent levels of cash flow (earnings). Price is the present value of expected future cash flows, so if cash flow volatility forecasts future cash flows (the numerator in the present value calculation), it should have valuation implications. A similar motivation applies to earnings, which may be viewed as a proxy for cash flow.

Pricing American options requires solving an optimal stopping problem and therefore presents a challenge for simulation. This article investigates connections between a weighted Monte Carlo technique and regression-based methods for this problem. The weighted Monte Carlo technique is shown to be equivalent to a least-squares method in which option values are regressed at a later time than in other regression-based methods.

Over the last three decades, there has been a substantial shift in financial market policy towards the promotion of financial liberalization. Policy makers around the globe have been preoccupied with deregulating interest rates, lifting restrictions on bank portfolios and enticing competition in financial services. Financial deregulation is typically accompanied with a change in the system of prudential regulation.