This paper considers a decentralized supply chain including one retailer and one manufacturer , where the manufacturer's production yield and the retailer's demand are both sto-chastic. At the beginning of the selling season, the retailer places an order and purchases an option contract with the manufacturer. After the selling season, the excess demand is partially backordered, and the retailer...

We use a notion of stochastic time, here called volatility time, to show convexity of option prices in the underlying asset if the contract function is convex as well as continuity and monotonicity of the option price in the volatility. The volatility time is obtained as the almost surely unique stopping time solution to a random ordinary differential equation related to volatility. This enable...

We use a notion of stochastic time, here called volatility time, to show convexity of option prices in the underlying asset if the contract function is convex as well as continuity and monotonicity of the option price in the volatility. The volatility time is obtained as the almost surely unique stopping time solution to a random ordinary differential equation related to volatility. This enable...

financial derivatives are new instruments through which hedging, investment and arbitrage are done in a modern economy. although the word 'derivative'primarily reminds us of options and futures, the major focus of the equity derivatives industry worldwide is on index derivatives. launching index options and index futures in tehran stock exchange, not only increases financial market de...

We prove that the perpetual American put option price of an exponential Lévy process whose jumps come from a compound Poisson process is the classical solution of its associated quasi-variational inequality, that it is C except at the stopping boundary and that it is C everywhere (i.e. the smooth pasting condition always holds). We prove this fact by constructing a sequence of functions, each o...

We prove that the perpetual American put option price of an exponential Lévy process whose jumps come from a compound Poisson process is the classical solution of its associated quasi-variational inequality, that it is C except at the stopping boundary and that it is C everywhere (i.e. the smooth pasting condition always holds). We prove this fact by constructing a sequence of functions, each o...

We prove that the perpetual American put option price of an exponential Lévy process whose jumps come from a compound Poisson process is the classical solution of its associated quasi-variational inequality, that it is C except at the stopping boundary and that it is C everywhere (i.e. the smooth pasting condition always holds). We prove this fact by constructing a sequence of functions, each o...

This work is devoted to the discrete time hedging of the American option on a dividendpaying stock with a convex payoff, the particular case of which is American call option. Perfect hedging requires continuous trading in time and knowledge of the partial derivative of the value function of the American option in the underlying asset. Neither one can trade continuously in time nor the closed-fo...

We develop an option model to quantify and price a flexible supply contract, by which the buyer (a manufacturer), in addition to a committed order quantity, can purchase option contracts and decide whether or not to exercise them after demand is realized. We consider both call and put options, which generalize several widely practiced contracting schemes such as capacity reservation and buy-bac...

In this article, we model money-back guarantees (MBGs) as put options. This use of option theory provides retailers with a framework to optimize the price and the return option independently and under various market conditions. This separation of product price and option value enables retailers to offer an unbundled MBG policy, that is, to allow the customer to choose whether to purchase an MBG...