In this paper, in order to model breach of contract risk, we design and value a bundled option that is composed of contract abandonment and price renegotiation. We show numerically that the bundled option is more valuable for the contract than either of the options, ie, contract abandonment and price renegotiation, in isolation. This value increases monotonically as the spot price becomes more ...

We consider hedging of a path-dependent European style option with convex continuous payoff in a discrete time incomplete market, where underlying stock price jumps are distributed over a bounded interval. The incompleteness of the market produces an interval of no-arbitrage option prices for the path-dependent option. Upper and lower bounds for the noarbitrage price interval are developed. Exp...

Repricing of an employee stock option refers to the practice of lowering the strike price and /or extending the maturity date of a previously granted employee stock option. Normally, firms reprice after a period of significant stock price decline that renders the employee stock options deeply out-of-the-money. By modeling various repricing mechanisms based on some form of Brownian functional of...

The problem of determining the European-style option price in the incomplete market has been examined within the framework of stochastic optimization. An analytic method based on the discrete dynamic programming equation (Bellman equation) has been developed that gives the general formalism for determining the option price and the optimal trading strategy (optimal control policy) that reduces t...

The problem of determining the European-style option price in the incomplete market has been examined within the framework of stochastic optimization. An analytic method based on the discrete dynamic programming equation (Bellman equation) has been developed that gives the general formalism for determining the option price and the optimal trading strategy (optimal control policy) that reduces t...

Decision tree analysis involves forecasting future outcomes and assigning probabilities to those events. One of the most basic fundamental applications of decision tree analysis is for the purpose of option pricing. The binomial tree would factor in multiple paths that the underlying asset's price can take as time progresses. The price of the option is calculated using the discrete probabilitie...

One of the most widely studied problems in financial mathematics is the pricing of derivative securities, also known as contingent claims. These are securities whose price depend on the value of another underlying security. Financial options are the most common examples of derivative securities. For example, a European call option on a particular underlying security gives the holder the right t...

Consider the European call option written on a zero-coupon bond. Suppose the call option has maturity T and strike price K while the bond has maturity S>T. We propose a numerical method for evaluating the call option price under the Chan, Karolyi, Longstaff and Sanders (CKLS) model in which the increment of the short rate over a time interval of length dt, apart from being independent and stati...

Option trading forms part of our financial markets. A traded option gives to its owner the right to buy (call option) or to sell (put option) a fixed quantity of assets of a specified stock at a fixed price (exercise or strike price). There are two major types of traded options. One is the American option that can be exercised at any time prior to its expiry date, and the other option, which ca...