Alfredo Ibáñez

MONTE CARLO VALUATION OF AMERICAN OPTIONS THROUGH COMPUTATION OF THE OPTIMAL EXERCISE FRONTIER

This paper introduces a Monte Carlo simulation method for pricing multidimensional American options. The method is based on the computation of the optimal exercise frontier. It is simple, efficient and flexible, suitable for multidimensional options. We consider options that can be exercised at a finite number of points, and compute the points of the exercise frontier recursively. We introduce an algorithm that converges very quickly to the value of the optimal exercise frontier.For multidimensional options, we fix the values of all the paramethers but one (usually the underlying security) and compute the value of the underlying at the optimal exercise frontier. Since the method converges very quickly, it is relatively fast (at least for low-dimensional options) to construct a grid for the frontier. One of the advantages of computing the optimal exercise frontier is that it can be used in subsequent computations that will only require application of plain vanilla Monte Carlo simulationThe method also allows a quick computation of the hedging portfolio. We present examples and we compare the numbers we get to other existing papers and show that at a low computational cost our results are as good as the best with the advantage that we simultaneously compute the optimal exercise frontier (which will simplify further any subsequent computations).

When can you immunize a bond portfolio

The object of this paper is to give conditions under which it is possible to immunize a bond portfolio. Maxmin strategies are also studied, as well as their relations with immunized ones. Some special shocks on the interest rate are analyzed, and general conditions about immunization are obtained. When immunization is not possible, capital losses are measured.

Robust Pricing of the American Put Option: A Note on Richardson Extrapolation and the Early Exercise Premium

This paper presents a detailed analysis of the numerical implementation of the American put option decomposition into an equivalent European option plus an early exercise premium (Kim 1990, Jacka 1991, Carr et al. 1992). It subsequently introduces a new algorithm based upon this decomposition and Richardson extrapolation. This new algorithm is based upon (a) the derivation of the correct order for the error term when applying Richardson extrapolation, which is used to control the error of the extrapolated prices, (b) an innovative adjustment of Kims (1990) discrete-time early exercise premium, so that these premiums monotonically converge and, therefore, it is appropriate to use them in extrapolation, and (c) the optimal exercise frontier can be quickly computed through Newtons method, permitting the efficient implementation of the decomposition formula in practice. Numerical experiments show that this new algorithm is accurate, efficient, easy to implement, and competitive in comparison with other methods. Finally, it can also be applied to other American exotic securities.

Dispersion measures as immunization risk measures

The quadratic and linear cash flow dispersion measures M 2 and ~ N are two immunization risk measures designed to build immunized bond portfolios. This paper generalizes these two measures by showing that any dispersion measure is an immunization risk measure and therefore, it sets up a tool to be used in empirical testing. Each new measure is derived from a different set of shocks (changes on the term structure of interest rates) and depends on the corresponding subset of worst shocks. Consequently, a criterion for choosing appropriate immunization risk measures is to take those developed from the most reasonable sets of shocks and the associated subset of worst shocks and then select those that work best empirically. Adopting this approach, this paper then explores both numerical examples and a short empirical study on the Spanish Bond Market in the mid-1990s to show that measures between linear and quadratic are the most appropriate, and amongst them, the linear measure has the best properties. This confirms previous studies on US and Canadian markets that maturityconstrained-duration-matched portfolios also have good empirical behavior. 2002 Elsevier Science B.V. All rights reserved.

Recursive Lower- and Dual Upper-Bounds for Bermudan-Style Options

Bermudan-style options are priced by simulation by computing lower- and (dual) upper-bounds. However, much less is known about the associated two optimal bounds. This paper adresses this gap and shows that the exercise strategy that maximizes the Bermudan price (Ibanez and Velasco (2016) local least-squares method) also minimizes (no the dual upper-bound itself, but) the gap between the lower- and the upper-bound in a recursive way. We then price Bermudan max-call options with an up-and-out barrier, which is a difficult stopping-time problem, reducing the gap produced by state-of-the-art methods (including least-squares and pathwise optimization) from 200 basis points -- or more to just one figure. Our results indicate that upper-bounds are tighter than lower-bounds, and hence a mid-point will be lower biased (contrary to conventional wisdom).

On the Negative Market Volatility Risk-Premium: Bridging the Gap Between Option Returns and the Pricing of Options

Existing evidence indicates that (i) average returns of purchased delta-hedged options are negative, implying options are expensive, and (ii) volatility is the most important extra risk that is factored into option prices. Therefore, a natural extension is to explain the cross-section of average delta-hedged option returns in a stochastic volatility model. This paper solves this problem by introducing a measure of option overprice, which quantifies the impact on option prices of the volatility risk premium. It is an application of option-pricing in incomplete markets under stochastic volatility. An extensive numerical exercise shows the option overprice is consistent with the cross-section of average delta-hedged returns of calls, puts, and straddles reported by the literature for the S&P 500 index, except for expensive short-term out-of-the-money puts. In a stochastic volatility model, the volatility risk of at- and, especially, out-of-the-money calls and puts is several times larger than market volatility, which explains large negative volatility risk premiums if volatility risk is negative priced.

Maxmin Portfolios in Models Where Immunization is Not Feasible

This work illustrates the difference between the concepts of immunized and maxmin portfolios and extends the existent literature on bond portfolio immunization by analyzing and computing maxmin portfolios in models where complete immunization is not feasible. These models are important because they permit many different shifts on interest rates and do not lead to the existence of arbitrage. Maxmin portfolios are characterized by saddle point conditions and can be computed by applying a new algorithm. The model is specialized on the very general sets of shocks from which the dispersion measures M 2 and N are developed. By computing maxmin portfolios in some practical examples, it is shown that they perform close to an immunized portfolio and are close to matching duration portfolios. Consequently, maxmin portfolios provide hedging strategies in a very general setting and can answer some puzzles of this literature.