Hedging a derivative security with non-risk-neutral number of shares leads to portfolio profit or loss. Unlike in the Black-Scholes world, the net present value of all future cash flows till maturity is no longer deterministic, and basis risk may be present at any time. The key object of our analysis is probability distribution of future P&L conditioned on the present value of the underlying. W...

We consider the robust hedging problem in which an investor wants to super-hedge an option in the framework of uncertainty in a model of a stock price process. More specifically, the investor knows that the stock price process is H -self-similar with H ∈ (1/2, 1), and that the log-returns are Gaussian. This leads to two natural but mutually exclusive hypotheses both being self-contained to fix ...

American options are studied in a general discrete market in the presence of proportional transaction costs, modelled as bid-ask spreads. Pricing algorithms and constructions of hedging strategies, stopping times and martingale representations are presented for short (seller’s) and long (buyer’s) positions in an American option with an arbitrary payoff. This general approach extends the special...

The Geske-Johnson approach provides an e cient and intuitively appealing technique for the valuation and hedging of American-style contingent claims. Here, we generalize their approach to a stochastic-interest-rate economy. The method is implemented using options exercisable on one of a nite number of dates. We illustrate how the value of an American-style option increases with interest-rate vo...

Abstract: The virtue of an American option is that it can be exercised at any time. This right is particularly valuable when there is model uncertainty. Yet almost all the extensive literature on American options assumes away model uncertainty. This paper quantifies the potential value of this flexibility by identifying the supremum on the price of an American option when no model is imposed on...

The goal of this paper is to show that the jump-diffusion models are an essential and easy-to-learn tool for option pricing and risk management, and that they provide an adequate description of stock price fluctuations and market risks. We try to give an overview of the field without focusing on technical details. After introducing several widely used jump-diffusion models, we discuss Fourier t...

We study the integrated operational and financial hedging decisions faced by a global firm who sells to both home and foreign markets. Production occurs either at a single facility located in one of the markets or at two facilities, one in each market. The company has to invest in capacity before the selling season starts when the demand in both markets and the currency exchange rate are uncert...

This thesis contains three essays on option pricing. The first discusses a way to measure the risk of the short trader of an option if he decides to hedge partially his position. The second deals with the pricing of American-style Asian options, and the third with call and put options embedded in bonds. The first essay considers the case of a short trader of an option who decides to partially h...

We reconsider the problem of option pricing using historical probability distributions. We first discuss how the risk-minimisation scheme proposed recently is an adequate starting point under the realistic assumption that price increments are uncorrelated (but not necessarily independent) and of arbitrary probability density. We discuss in particular how, in the Gaussian limit, the Black-Schole...

Hedging is no longer an option for multinational corporations, especially during global financial crisis. This was clearly manifested in companies’ comprehensive income statement as in WalMart’s case that “During fiscal 2009, foreign currency exchange rate had a $2.3 billion unfavorable impact on the international segment’s net sales” and the company just lost $680 million in the second quarter...