Browsing by Subject "Martingales"

Now showing 1 - 8 of 8

Open Access
The Best Gain-Loss Ratio is a Poor Performance Measure
(Society for Industrial and Applied Mathematics, 2013-03-06) Biagini, S.; Pinar, M. Ç.
The gain-loss ratio is known to enjoy very good properties from a normative point of view. As a confirmation, we show that the best market gain-loss ratio in the presence of a random endowment is an acceptability index, and we provide its dual representation for general probability spaces. However, the gain-loss ratio was designed for finite Ω and works best in that case. For general Ω and in most continuous time models, the best gain-loss is either infinite or fails to be attained. In addition, it displays an odd behavior due to the scale invariance property, which does not seem desirable in this context. Such weaknesses definitely prove that the (best) gain-loss is a poor performance measure.
Open Access
Expected gain-loss pricing and hedging of contingent claims in incomplete markets by linear programming
(Elsevier, 2010) Pınar, M. Ç.; Salih, A.; Camcı, A.
We analyze the problem of pricing and hedging contingent claims in the multi-period, discrete time, discrete state case using the concept of a "λ gain-loss ratio opportunity". Pricing results somewhat different from, but reminiscent of, the arbitrage pricing theorems of mathematical finance are obtained. Our analysis provides tighter price bounds on the contingent claim in an incomplete market, which may converge to a unique price for a specific value of a gain-loss preference parameter imposed by the market while the hedging policies may be different for different sides of the same trade. The results are obtained in the simpler framework of stochastic linear programming in a multi-period setting, and have the appealing feature of being very simple to derive and to articulate even for the non-specialist. They also extend to markets with transaction costs.
Open Access
Financial valuation of supply chain contracts
(John Wiley & Sons, 2011) Pınar, Mustafa Ç.; Şen, Alper; Erön, A. G.; Kouvelis, P.; Dong, L.; Boyabatli, O.; Li, R.
This chapter focuses on a single buyer‐single supplier multiple period quantity flexibility contract in which the buyer has options to order additional quantities of goods in case of a higher than expected demand in addition to the committed purchases at the beginning of each period of the contract. It takes the buyer’s point of view and finds the maximum value of the contract for the buyer by analyzing the financial and real markets simultaneously. The chapter assumes both markets evolve as discrete scenario trees. Under the assumption that the demand of the item is perfectly positively correlated with the price of a risky security traded in the financial market, the chapter presents a model to find the buyer’s maximum acceptable price of the contract. Applying duality theory of linear programming, the chapter obtains a martingale expression for the value of the contract.
Open Access
Gain-loss pricing under ambiguity of measure
(E D P Sciences, 2010) Pınar, M. Ç.
Motivated by the observation that the gain-loss criterion, while offering economically meaningful prices of contingent claims, is sensitive to the reference measure governing the underlying stock price process (a situation referred to as ambiguity of measure), we propose a gain-loss pricing model robust to shifts in the reference measure. Using a dual representation property of polyhedral risk measures we obtain a one-step, gain-loss criterion based theorem of asset pricing under ambiguity of measure, and illustrate its use.
Open Access
An integer programming model for pricing American contingent claims under transaction costs
(2012) Pınar, M. Ç.; Camcı, A.
We study the problem of computing the lower hedging price of an American contingent claim in a finite-state discrete-time market setting under proportional transaction costs. We derive a new mixed-integer linear programming formulation for calculating the lower hedging price. The linear programming relaxation of the formulation is exact in frictionless markets. Our results imply that it might be optimal for the holder of several identical American claims to exercise portions of the portfolio at different time points in the presence of proportional transaction costs while this incentive disappears in their absence.
Open Access
Lower hedging of American contingent claims with minimal surplus risk in finite-state financial markets by mixed-integer linear programming
(2014) Pınar, M. Ç.
The lower hedging problem with a minimal expected surplus risk criterion in incomplete markets is studied for American claims in finite state financial markets. It is shown that the lower hedging problem with linear expected surplus criterion for American contingent claims in finite state markets gives rise to a non-convex bilinear programming formulation which admits an exact linearization. The resulting mixed-integer linear program can be readily processed by available software.
Open Access
Pricing American contingent claims by stochastic linear programming
(Taylor & Francis, 2009) Camcı, A.; Pınar, M. Ç.
We consider pricing of American contingent claims (ACC) as well as their special cases, in a multi-period, discrete time, discrete state space setting. Until now, determining the buyer's price for ACCs required solving an integer programme unlike European contingent claims for which solving a linear programme is sufficient. However, we show that a relaxation of the integer programming problem that is a linear programme, can be used to get the same lower bound for the price of the ACC.
Open Access
Sharpe-ratio pricing and hedging of contingent claims in incomplete markets by convex programming
(Elsevier, 2008-08) Pınar, M. Ç.
We analyze the problem of pricing and hedging contingent claims in a financial market described by a multi-period, discrete-time, finite-state scenario tree using an arbitrage-adjusted Sharpe-ratio criterion. We show that the writer’s and buyer’s pricing problems are formulated as conic convex optimization problems which allow to pass to dual problems over martingale measures and yield tighter pricing intervals compared to the interval induced by the usual no-arbitrage price bounds. An extension allowing proportional transaction costs is also given. Numerical experiments using S&P 500 options are given to demonstrate the practical applicability of the pricing scheme.