I use a new technique to derive a closed-form solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and spotasset returns. I introduce stochastic interest rates and show how to apply the model to bond options and foreign currency options. Simulations show that correlation between volatility and the spot asset’s price is important for explaining return skewness and strike-price biases in the BlackScholes (1973) model. The solution technique is based on characteristi c functions and can be applied to other problems.

/pdf/a-closed-form-solution-for-options-with-stochastic-2mnz9ol71o.pdf

A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options

We present a consumption-based model that explains a wide variety of dynamic asset pricing phenomena, including the procyclical variation of stock prices, the long-horizon predictability of excess stock returns, and the countercyclical variation of stock market volatility The model captures much of the history of stock prices from consumption data It explains the short- and long-run equity premium puzzles despite a low and constant risk-free rate The results are essentially the same whether we model stocks as a claim to the consumption stream or as a claim to volatile dividends poorly correlated with consumption The model is driven by an independently and identically distributed consumption growth process and adds a slow-moving external habit to the standard power utility function These features generate slow countercyclical variation in risk premia The model posits a fundamentally novel description of risk premia: Investors fear stocks primarily because they do poorly in recessions unrelated to the risks of long-run average consumption growth

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By Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior

"Dynamic Asset Pricing Theory" is a textbook for doctoral students and researchers on the theory of asset pricing and portfolio selection in multiperiod settings under uncertainty. The asset pricing results are based on the three increasingly restrictive assumptions: absence of arbitrage, single-agent optimaltiy, and equilibrium. These results are unified with two key concepts, state prices and martingales. Technicalities are given relatively little emphasis so as to draw connections between these concepts and to make plain the similarities between discrete and continuous-time models. For simplicity, all continuous-time models are based on Brownian motion. Applications include term structure models, derivative valuation and hedging methods, and dynamic programming algorithms for portfolio choice and optimal exercise of American options. Numerical methods covered include Monte Carlo simulation and finite-difference solvers for partial differential equations. Each chapter provides extensive problem exercises and notes to the literature. This second edition is substantially longer, while still retaining the consciseness for which the first edition was praised. All chapters from the first edition have been revised. Two new chapters have been added on term structure modeling and on derivative securities. References have been updated throughout. With this new edition, "Dynamic Asset Pricing Theory" remains the definitive textbook in the field.

https://epge.fgv.br/we/MD/Financas/2012?action=AttachFile&do=get&target=DuffieChap1.pdf

Dynamic Asset Pricing Theory

Substantial progress has been made in developing more realistic option pricing models. Empirically, however, it is not known whether and by how much each generalization improves option pricing and hedging. We fill this gap by first deriving an option model that allows volatility, interest rates and jumps to be stochastic. Using S&P 500 options, we examine several alternative models from three perspectives: (1) internal consistency of implied parameters/volatility with relevant timeseries data, (2) out-of-sample pricing, and (3) hedging. Overall, incorporating stochastic volatility and jumps is important for pricing and internal consistency. But for hedging, modeling stochastic volatility alone yields the best performance. IN THE LAST TWO DECADES, option pricing has witnessed an explosion of new

/pdf/empirical-performance-of-alternative-option-pricing-models-18wa1txytu.pdf

Empirical Performance of Alternative Option Pricing Models

https://teach.business.uq.edu.au/courses/FINM6900/files/module-2/readings/BreedenJFE.pdf

An intertemporal asset pricing model with stochastic consumption and investment opportunities

This paper uses an intertemporal general equilibrium asset pricing model to study the term structure of interest rates. In this model, anticipations, risk aversion, investment alternatives, and preferences about the timing of consumption all play a role in determining bond prices. Many of the factors traditionally mentioned as influencing the term structure are thus included in a way which is fully consistent with maximizing behavior and rational expectations. The model leads to specific formulas for bond prices which are well suited for empirical testing. 1. INTRODUCTION THE TERM STRUCTURE of interest rates measures the relationship among the yields on default-free securities that differ only in their term to maturity. The determinants of this relationship have long been a topic of concern for economists. By offering a complete schedule of interest rates across time, the term structure embodies the market's anticipations of future events. An explanation of the term structure gives us a way to extract this information and to predict how changes in the underlying variables will affect the yield curve. In a world of certainty, equilibrium forward rates must coincide with future spot rates, but when uncertainty about future rates is introduced the analysis becomes much more complex. By and large, previous theories of the term structure have taken the certainty model as their starting point and have proceeded by examining stochastic generalizations of the certainty equilibrium relationships. The literature in the area is voluminous, and a comprehensive survey would warrant a paper in itself. It is common, however, to identify much of the previous work in the area as belonging to one of four strands of thought. First, there are various versions of the expectations hypothesis. These place predominant emphasis on the expected values of future spot rates or holdingperiod returns. In its simplest form, the expectations hypothesis postulates that bonds are priced so that the implied forward rates are equal to the expected spot rates. Generally, this approach is characterized by the following propositions: (a) the return on holding a long-term bond to maturity is equal to the expected return on repeated investment in a series of the short-term bonds, or (b) the expected rate of return over the next holding period is the same for bonds of all maturities. The liquidity preference hypothesis, advanced by Hicks [16], concurs with the importance of expected future spot rates, but places more weight on the effects of the risk preferences of market participants. It asserts that risk aversion will cause forward rates to be systematically greater than expected spot rates, usually

https://pages.stern.nyu.edu/~dbackus/BCZ/discrete_time/CIR_Econometrica_85.pdf

Ingersoll Jonathan E

Papers

A Theory of the Term Structure of Interest Rates.