Journal•ISSN: 1350-486X
Applied Mathematical Finance
Chapman and Hall London
About: Applied Mathematical Finance is an academic journal published by Chapman and Hall London. The journal publishes majorly in the area(s): Stochastic volatility & Valuation of options. It has an ISSN identifier of 1350-486X. Over the lifetime, 497 publications have been published receiving 14293 citations.
Topics: Stochastic volatility, Valuation of options, Implied volatility, Volatility (finance), Volatility smile
Papers published on a yearly basis
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TL;DR: In this paper, the authors present a model for pricing and hedging derivative securities and option portfolios in an environment where the volatility is not known precisely, but is assumed instead to lie between two extreme values σmin and σmax.
Abstract: We present a model for pricing and hedging derivative securities and option portfolios in an environment where the volatility is not known precisely, but is assumed instead to lie between two extreme values σminand σmax. These bounds could be inferred from extreme values of the implied volatilities of liquid options, or from high-low peaks in historical stock- or option-implied volatilities. They can be viewed as defining a confidence interval for future volatility values. We show that the extremal non-arbitrageable prices for the derivative asset which arise as the volatility paths vary in such a band can be described by a non-linear PDE, which we call the Black-Scholes-Barenblatt equation. In this equation, the ‘pricing’ volatility is selected dynamically from the two extreme values, σmin, σmax, according to the convexity of the value-function. A simple algorithm for solving the equation by finite-differencing or a trinomial tree is presented. We show that this model captures the importance of diversifi...
728 citations
TL;DR: In this paper, the authors consider the problem of liquidating a large single-asset portfolio to minimize a combination of volatility risk and market impact costs, with an arbitrary positive exponent.
Abstract: Optimal trading strategies are determined for liquidation of a large single-asset portfolio to minimize a combination of volatility risk and market impact costs. The market impact cost per share is taken to be a power law function of the trading rate, with an arbitrary positive exponent. This includes, for example, the square root law that has been proposed based on market microstructure theory. In analogy to the linear model, a ‘characteristic time’ for optimal trading is defined, which now depends on the initial portfolio size and decreases as execution proceeds. A model is also considered in which uncertainty of the realized price is increased by demanding rapid execution; it is shown that optimal trajectories are described by a ‘critical portfolio size’ above which this effect is dominant and below which it may be neglected.
522 citations
TL;DR: In this article, a mean-reverting jump diffusion model for the electricity spot price and the corresponding forward price in closed-form was presented. But the model was not calibrated and months, quarters, and seasons-ahead forward surfaces were presented.
Abstract: This paper presents a mean‐reverting jump diffusion model for the electricity spot price and derives the corresponding forward price in closed‐form. Based on historical spot data and forward data from England and Wales the model is calibrated and months, quarters, and seasons–ahead forward surfaces are presented.
401 citations
TL;DR: In this paper, the authors introduce optimal and risk-free strategies for intermediaries in a multidimensional frictionless security market to meet their obligations when the volatility is unknown, and is only assumed to lie in some convex region depending on the prices of the underlying securities and time.
Abstract: To price contingent claims in a multidimensional frictionless security market it is sufficient that the volatility of the security process is a known function of price and time. In this note we introduce optimal and risk-free strategies for intermediaries in such markets to meet their obligations when the volatility is unknown, and is only assumed to lie in some convex region depending on the prices of the underlying securities and time. Our approach is underpinned by the theory of totally non-linear parabolic partial differential equations (Krylov and Safanov, 1979; Wang, 1992) and the non-stochastic approach to Ito's formation first introduced by Follmer (1981a,b). In these more general conditions of unknown volatility, the optimal risk-free trading strategy will, necessarily, produce an unpredictable surplus over the minimum assets required at any time to meet the liabilities. This surplus, which could be released to the intermediary or to the client, is not required to meet the contingent claim. One s...
383 citations
TL;DR: In this article, the main objective of the work described is to find a pricing model for weather derivatives with payouts depending on temperature, using historical data to suggest a stochastic process that describes the evolution of the temperature.
Abstract: The main objective of the work described is to find a pricing model for weather derivatives with payouts depending on temperature. Historical data are used to suggest a stochastic process that describes the evolution of the temperature. Since temperature is a non-tradable quantity, unique prices of contracts in an incomplete market are obtained using the market price of risk. Numerical examples of prices of some contracts are presented, using an approximation formula as well as Monte Carlo simulations.
380 citations