Browsing by Subject "martingales"

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Open Access
A dual representation of gain-loss hedging for European claims in discrete time
(2012) Pinar, M.C.
Superhedging of European claims in incomplete markets is a well-studied problem. The superhedging value of a European claim is known to yield a price too large to be interesting in some cases. In this note, an alternative hedging strategy based on an expected gain-loss criterion is studied for European claims in infinite state space, discrete time financial markets. A dual representation for the gain-loss hedging value is obtained. © 2012 Copyright Taylor and Francis Group, LLC.
Open Access
Financial valuation of flexible supply chain contracts
(2008) Erön, Ali Gökay
We consider a single buyer - single supplier multiple period quantity flexibility contract in which the buyer has options to buy in case of a higher than expected demand in addition to the committed purchases at the beginning of each period of the contract. We take the buyer’s point of view and find the maximum value of the contract for the buyer by analyzing the financial and real markets simultaneously. We assume both markets evolve as discrete scenario trees. Furthermore, under the assumption that the demand of the item correlates perfectly with the price of the risky security we present a model to find the buyer’s maximum acceptable price of the contract. Applying duality, we develop sufficient conditions on some parameters to decrease the value of the contract. Then, an experimental study is presented to illustrate the impacts of all the parameters on the value of the contract and the option. We show that the model can also be extended to the case of partially correlated demand and the risky asset price under the assumption that the markets evolve as binomial trees. Finally, we apply duality and perform numerical analysis for the latter assumption.
Open Access
Pricing and hedging of contingent claims in incopmplete markets by modeling losses as conditional value at risk in (formula)-gain loss opportunities
(2009) Aydın, Zeynep
We combine the principles of risk aversion and no-arbitrage pricing and propose an alternative way for pricing and hedging contingent claims in incomplete markets. We re-consider the pricing problem under the condition that losses are modeled by the measure of CVaR in the concept of λ gain-loss opportunities. The proposed model enables investors to specify their preferences by putting restrictions on the parameter λ that stands for risk aversion. Using CVaR as a measure of risk enables us to account for extreme losses and yield a conservative result. The pricing problem is studied in discrete time, multi-period, stochastic linear optimization environment with a finite probability space. We extend our model to include the perspectives of writers and buyers of the contingent claims. We use duality to establish a pricing interval of the contingent claims excluding CVaR-λ gain-loss opportunities in the market. Duality results also provide a way for passing to appropriate martingale measures and we express the pricing interval also in terms of martingale measures. This pricing interval is shown to be tighter than the no-arbitrage bounds. We also present a numerical study of our work with respect to the risk aversion parameter λ and in various levels of confidence. We compute prices of the the writers and buyers of 48 European call and put options on the S&P500 index on September 10, 2002 using the remaining options as market traded assets. It is possible to say that our proposed model yields good bounds as most of the bounds we obtained are very close to the true bid and ask values.