Traditional plain vanilla options can be regarded as options on a simple return. These options have convex payoffs and as a consequence of Jensen's inequality, their prices are increasing as a function of maturity in the absence of interest rate. This makes long dated call options as excessively...

… a nice book for researchers and practitioners. … this book can be regarded as a wonderful application of stochastic analysis, as it includes not only detailed theoretical proofs but also practical illustrative examples. With the systematic and feasible numeraire techniques, the book can...

chapter 1 Elements of Finance -- chapter 2 Binomial Models -- chapter 3 Diffusion Models -- chapter 4 Interest Rate Contracts -- chapter 5 Barrier Options -- chapter 6 Lookback Options -- chapter 7 American Options -- chapter 8 Contracts on Three or More Assets: Quantos, Rainbows and "Friends"...

The contracts written on the harmonic average of the underlying price are quite popular in the foreign exchange market. If X denotes the foreign currency and Y denotes the domestic currency, the payoff of the contract is a function of a price of an asset H which is defined asH(T) =...

This paper considers multiple market agents who have distinct distributional opinions about the state price density. Different opinions can be contested on a hypothetical market that trades Arrow-Debreu securities. We focus on the situation when the agents are maximizing logarithmic utility as...

Asian options are securities with a payoff that depends on the average of the underlying stock price over a certain time interval. We identify three natural assets that appear in pricing of the Asian options, namely a stock S, a zero coupon bond BT with maturity T, and an abstract asset A (an...