This paper develops a Monte Carlo simulation method for solving option valuation problems. The method simulates the process generating the returns on the underlying asset and invokes the risk neutrality assumption to derive the value of the option. Techniques for improving the efficiency of the method are introduced. Some numerical examples are given to illustrate the procedure and additional applications are suggested.
This paper analyzes the optimal portfolio choice problem when security returns have a joint multivariate normal distribution with unknown parameters. For the case of limited, but sufficient (sample plus prior) information, we show that for a general family of conjugate priors, the optimal portfolio choice is obtained by the use of a mean-variance analysis that differs from traditional mean-variance analysis due to estimation risk. We also consider two illustrative cases of insufficient sample information and minimal prior information and show that in these cases it is asymptotically optimal for an investor to limit diversification to a subset of the securities. These theoretical results corroborate observed investor behavior in capital markets.
Testing the two-parameter asset pricing theory is difficult (and currently infeasible). Due to a mathematical equivalence between the individual return/‘beta’ linearity relation and the market portfolio's mean-variance efficiency, any valid test presupposes complete knowledge of the true market portfolio's composition. This implies, inter alia, that every individual asset must be included in a correct test. Errors of inference inducible by incomplete tests are discussed and some ambiguities in published tests are explained.
In this paper large block stock transactions are examined in the context of a trading rule devised by Grier and Albin. The study makes use of the actual intra-day history of stock transactions. Considerable effort is taken to correctly incorporate the effects of transaction costs on trading rule profits and evidence is presented on the sensitivity of such profits to variations in these costs. The use of intra-day prices yields results consistent with the weak form of the efficient markets hypothesis and provides important evidence on the speed of price adjustment.
Many corporate assets, particularly growth opportunities, can be viewed as call options. The value of such ‘real options’ depends on discretionary future investment by the firm. Issuing risky debt reduces the present market value of a firm holding real options by inducing a suboptimal investment strategy or by forcing the firm and its creditors to bear the costs of avoiding the suboptimal strategy. The paper predicts that corporate borrowing is inversely related to the proportion of market value accounted for by real options. It also rationalizes other aspects of corporate borrowing behavior, for example the practice of matching maturities of assets and debt liabilities.
This paper develops a new distribution theory for common stock returns. The model is composed of a calendar time diffusion process and a jump process where the magnitudes of the jumps may be autocorrelated. Empirical tests are performed on a month of transactions returns for twenty New York Stock Exchange securities. The data analysis supports the validity of the proposed theory.
This paper examines the relationship between forward exchange rates and subsequently observed spot rates. No evidence is found for a liquidity premium on forward exchange, indicating that the forward rate can be used as a proxy of the market's expectations and that open exchange positions involve little systematic risk. It is also shown that forward exhange is priced as if the exchange rate could be characterized by a diffusion process with a trend, although there is some evidence such a process does not adequately characterize the exchange rate in all cases.
This paper examines the problem of deriving Black's (1972) minimum-variance zero-beta portfolio. Long's (1971) methods, used by Morgan (1975), are briefly mentioned. Then the complementary pivot algorithm of Lemke (1965), which has been shown to be capable of deriving the optimal solution to certain quadratic programming problems that are subject to a non-negativity constraint, is described. Finally, Lemke's algorithm is shown to be capable of deriving the minimum-variance zero-beta portfolio efficiently from samples of risky assets where both long and short positions are allowed by reformulating the problem so as to avoid the difficulties encountered by having a non-negatively constraint.
This paper is concerned with the valuation of multiperiod cash flows in a world where prices are determined according to the Sharpe-Lintner-Black model of capital market equilibrium. We find that the current market value of any future net cash flow is the current expected value of the flow discounted at risk-adjusted discount rates for each of the periods until the flow is realized. The discount rates are known and non-stochastic, but the rates for the different periods preceding the realization of a cash flow need not to be the same, and the rates relevant for a given period can differ across cash flows. The risk adjustments in the discount rates arise because of uncertainties about reassessments through time of the expected value of a flow and the relationships between these reassessments and the corresponding reassessments of the expected cash flows of all firms.