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We extend and unify Fourier-analytic methods for pricing a wide class of options on any underlying state variable whose characteristic function is known. In this general setting, we bound the numerical pricing error of discretized transform computations, such as DFT/FFT. These bounds enable algorithms to select efficient quadrature parameters and to price(More)
This paper derives in closed form the optimal dynamic portfolio policy when trading is costly and security returns are predictable by signals with different mean-reversion speeds. The optimal updated portfolio is a linear combination of the existing portfolio , the optimal portfolio absent trading costs, and the optimal portfolio based on future expected(More)
1 We study how intermediation and asset prices in over-the-counter markets are affected by illiquidity associated with search and bargaining. We compute explicitly the prices at which investors trade with each other, as well as marketmakers' bid and ask prices, in a dynamic model with strategic agents. Bid–ask spreads are lower if investors can more easily(More)
Consider options on a nonnegative underlying random variable with arbitrary distribution. In the absence of arbitrage, we show that at any maturity T , the large-strike tail of the Black-Scholes implied volatility skew is bounded by the square root of 2|x|/T , where x is log-moneyness. The smallest coefficient that can replace the 2 depends only on the(More)
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Bill Zame, and four anonymous referees for very helpful discussions and comments. Preliminary versions of this paper were presented at Abstract We prove existence of equilibrium in a continuous-time securities market in which the securities are potentially dynamically complete: the number of securities is at least one more than the number of independent(More)
This paper describes a new continuous-time principal-agent model, in which the output is a diffusion process with drift determined by the agent's unobserved effort. The risk-averse agent receives consumption continuously. The optimal contract, based on the agent's continuation value as a state variable, is computed by a new method using a differential(More)
When economic capital is calculated using a portfolio model of credit value-at-risk, the marginal capital requirement for an instrument depends, in general, on the properties of the portfolio in which it is held. By contrast, ratings-based capital rules, including both the current Basel Accord and its proposed revision, assign a capital charge to an(More)
While American calls on non-dividend-paying stocks may be valued as European, there is no completely explicit exact solution for the values of American puts. We use a technique called randomization to value American puts and calls on dividend-paying stocks. This technique yields a new semiexplicit approximation for American option values in the(More)