Efficient option pricing with transaction costs

A fast numerical algorithm is developed to price European options with proportional transaction costs using the utility-maximization framework of Davis (1997). This approach allows option prices to be computed by solving the investor’s basic portfolio selection problem without insertion of the option payoff into the terminal value function. The properties of the value function can then be used to drastically reduce the number of operations needed to locate the boundaries of the no-transaction region, which leads to very efficient option valuation. The optimization problem is solved numerically for the case of exponential utility, and comparisons with approximately replicating strategies reveal tight bounds for option prices even as transaction costs become large. The computational technique involves a discrete-time Markov chain approximation to a continuous-time singular stochastic optimal control problem. A general definition of an option hedging strategy in this framework is developed. This involves calculating the perturbation to the optimal portfolio strategy when an option trade is executed

Migration, credit markets, moral hazard, interlinkage.

A fast numerical algorithm is developed to price European options with proportional transaction costs using the utility maximization framework of Davis (1997). This approach allows option prices to be computed by solving the investor's basic portfolio selection problem, without the inser- tion of the option payo into the terminal value function. The properties of the value function can then be used to drastically reduce the number of operations needed to locate the boundaries of the no transaction region, which leads to very e cient option valuation. The optimization problem is solved numerically for the case of exponential utility, and comparisons with approximately replicating strategies reveal tight bounds for option prices even as transaction costs become large. The computational tech- nique involves a discrete time Markov chain approximation to a continuous time singular stochastic optimal control problem. A general de nition of an option hedging strategy in this framework is developed. This involves calculating the perturbation to the optimal portfolio strategy when an option trade is execute

Option Pricing and Hedging with Small Transaction Costs

An investor with constant absolute risk aversion trades a risky asset with general It\^o-dynamics, in the presence of small proportional transaction costs. In this setting, we formally derive a leading-order optimal trading policy and the associated welfare, expressed in terms of the local dynamics of the frictionless optimizer. By applying these results in the presence of a random endowment, we obtain asymptotic formulas for utility indifference prices and hedging strategies in the presence of small transaction costs.Comment: 20 pages, to appear in "Mathematical Finance

Option pricing and hedging with minimum local expected shortfall

We propose a versatile Monte-Carlo method for pricing and hedging options when the market is incomplete, for an arbitrary risk criterion (chosen here to be the expected shortfall), for a large class of stochastic processes, and in the presence of transaction costs. We illustrate the method on plain vanilla options when the price returns follow a Student-t distribution. We show that in the presence of fat-tails, our strategy allows to significantly reduce extreme risks, and generically leads to low Gamma hedging. Similarly, the inclusion of transaction costs reduces the Gamma of the optimal strategy.Comment: 23 pages, 7 figures, 8 table

An Asian Option to the Valuation of Insurance Futures Contracts

While insurers have a variety of instruments readily available to hedge the risk of assets and interest rate sensitive liabilities, until recently reinsurance was the only mechanism for hedging underwriting risk. The insurance futures contracts introduced in December 1992 by the Chicago Board of Trade (CBOT) offer insurers an alternative to reinsurance as a hedging device for under-writing risk. These instruments have the usual features of liquidity, anonymity, and low transaction costs that characterize futures contracts. Unlike reinsurance, hedging through futures has the advantage of reversibility since any position may be closed before the maturity of the futures contract if the overall exposure of the insurer has diminished. Reversing a reinsurance transaction exposes the insurer to relatively high transactions costs as well as additional charges to protect the reinsurer against adverse selection. Because futures contracts are based on losses incurred by a pool of a least 10 insurance companies selected by the Insurance Services Officer, the potential for adverse selection and the accompanying administrative costs are greatly diminished relative to a reinsurance contract. Unlike most futures contracts traded on the CBOT, insurance futures are based on an accumulation of insurance loss payments over a period of time rather than the price of a commodity or asset at the end of a period of time. The classical relationships between the spot price and the futures price do not hold. The fact that the futures price at maturity will reflect a sum of claim payments entails a structural similarity between this contract and an Asian option, for which the underlying asset is an average, i.e., a sum of spot prices (up to a multiplicative constant). Thus, it would be incorrect to price these instruments using standard futures pricing techniques. Geman and Yor (1992, 1993) investigate the exact solution of this problem. The authors apply the Geman-Yor approach to the valuation of the insurance catastrophe futures contracts offered by the CBOT. In their model, the state variable is assumed to be a geometric Brownian motion - the claims process. The payoff on the insurance futures contract is determined by the accumulation or integral of the state variable. The authors believe there is a significant systematic component to insurance losses, especially those involving catastrophes. Insurers should be able to reduce risk by trading futures contracts. In their view the primary reason for limited trading of insurance futures is the lack of information on the loss index. There is very little information to support parameter estimation or to assist traders in forming expectations. In the authors' view, the CBOT's current offerings are unlikely to be successful unless the information problem is solved.

Study of the risk-adjusted pricing methodology model with methods of Geometrical Analysis

Families of exact solutions are found to a nonlinear modification of the Black-Scholes equation. This risk-adjusted pricing methodology model (RAPM) incorporates both transaction costs and the risk from a volatile portfolio. Using the Lie group analysis we obtain the Lie algebra admitted by the RAPM equation. It gives us the possibility to describe an optimal system of subalgebras and correspondingly the set of invariant solutions to the model. In this way we can describe the complete set of possible reductions of the nonlinear RAPM model. Reductions are given in the form of different second order ordinary differential equations. In all cases we provide solutions to these equations in an exact or parametric form. We discuss the properties of these reductions and the corresponding invariant solutions.Comment: larger version with exact solutions, corrected typos, 13 pages, Symposium on Optimal Stopping in Abo/Turku 200

Option Pricing with Transaction Costs Using a Markov Chain Approximation

An e cient algorithm is developed to price European options in the pres- ence of proportional transaction costs, using the optimal portfolio frame- work of Davis (1997). A fair option price is determined by requiring that an in nitesimal diversion of funds into the purchase or sale of options has a neutral e ect on achievable utility. This results in a general option pricing formula, in which option prices are computed from the solution of the investor's basic portfolio selection problem, without the need to solve a more complex optimisation problem involving the insertion of the op- tion payo into the terminal value function. Option prices are computed numerically using a Markov chain approximation to the continuous time singular stochastic optimal control problem, for the case of exponential utility. Comparisons with approximately replicating strategies are made. The method results in a uniquely speci ed option price for every initial holding of stock, and the price lies within bounds which are tight even as transaction costs become large. A general de nition of an option hedg- ing strategy for a utility maximising investor is developed. This involves calculating the perturbation to the optimal portfolio strategy when an option trade is executed

Understanding smart contracts as a new option in transaction cost economics

Among different concepts associated with the term blockchain, smart contracts have been a prominent one, especially popularized by the Ethereum platform. In this study, we unpack this concept within the framework of Transaction Cost Economics (TCE). This institutional economics theory emphasizes the role of distinctive (private and public) contract law regimes in shaping firm boundaries. We propose that widespread adoption of the smart contract concept creates a new option in public contracting, which may give rise to a smart-contract-augmented contract law regime. We discuss tradeoffs involved in the attractiveness of the smart contract concept for firms and the resulting potential for change in firm boundaries. Based on our new conceptualization, we discuss potential roles the three branches of government – judicial, executive, and legislative – in enabling and using this new contract law regime. We conclude the paper by pointing out limitations of the TCE perspective and suggesting future research directions