In this paper we study American put options on zero-coupon bonds under the CIR model of short interest rates. The uniqueness of the optimal exercise boundary and the solution existence and uniqueness of a degenerate parabolic free boundary problem are established. Numerical examples are also presented to confirm theoretical results.

We derive explicit formulas for time decay, θ, for the European call and put options at expiry, and use them to calculate analytical approximations to the price of the American put and early exercise boundary near expiry. We show that for many families of non-Gaussian processes used in empirical studies of financial markets, the early exercise boundary for the American put without dividends is ...

We investigate qualitative and quantitative behavior of a solution to the problem of pricing American style of perpetual put options. We assume the option price is a solution to a stationary generalized Black-Scholes equation in which the volatility may depend on the second derivative of the option price itself. We prove existence and uniqueness of a solution to the free boundary problem. We de...

We revisit the American put and call option valuation problems. We derive analytical formulas for the option prices and approximate ordinary differential equations for the optimal exercise boundaries. Numerical simulations yield accurate option prices and comparable computational speeds when benchmarked against the binomial method for calculating option prices. Our approach is based on the Mell...

URL: www.thejournalofcomputationalfinance.com Most contracts of barrier and lookback options specify discrete monitoring policies. However, unlike their continuous counterparts, discrete barrier and lookback options essentially have no analytical solution. For a broad class of models, including the classical Brownian model and jump-diffusion models, we show that the Laplace transforms of discre...

We examine the early exercise policies and pricing behaviors of one-asset American options with lookback payoff structures. The classes of option models considered include floating strike lookback options, Russian options, fixed strike lookback options and pricing model of dynamic protection fund. For each class of the American lookback options, we analyze the optimal stopping region, in partic...

We investigate the information content of the call (put) Early Exercise Premium, or EEP , defined as the normalized difference in prices between otherwise comparable American and European call (put) options. The call EEP specifically captures investors’ expectations about future lump sum dividend payments as well as other state variables such as conditional volatility and interest rates. From t...

We will in some places restrict attention to puts, by put-call parity: for realized variance options, a long-call short-put combination pays [X]T −Q, equal to a Q-strike variance swap; and for realized volatility options, a long-call short-put combination pays [X] T − Q1/2, equal to a Q1/2-strike volatility swap. Unlike variance swaps [EQF07/024, EQF07/045], which admit exact model-free (assumi...

This paper describes the Itô processes for the continuously compounded returns on European call and put stock options under the one-dimensional diffusion assumption and the Black Scholes pricing model. It uses the Itô processes to motivate discrete time approximations for the returns on calls and puts. Theses models are used in a simulation study to compute the probability of an option return v...

We present WESt, a visualization for surgery waiting times applied to the province of British Columbia (BC) in Canada. This project is motivated by the long waiting time for surgeries in BC, which has the potential to put patients in danger and put extra pressure on clinicians [2]. WESt helps patients select a hospital and a physician, and to explore their options to get their surgery as soon a...