Discrete Solutions for Barrier Options
نویسنده
چکیده
A barrier option is an otherwise vanilla call or put option with a strike of X but with an extra parameter B, the barrier: the option only comes into existence (is knocked in) or is terminated (is knocked out) if the spot price crosses the barrier during the life of the option. Because there is a positive probability (in either case) of worthlessness, these options are cheaper than the corresponding vanilla option, and hence possibly more attractive to the speculator.
منابع مشابه
Discrete Barrier and Lookback Options
Discrete barrier and lookback options are among the most popular path-dependent options in markets. However, due to the discrete monitoring policy almost no analytical solutions are available for them. We shall focus on the following methods for discrete barrier and lookback option prices: (1) Broadie–Yamamoto method based on fast Gaussian transforms. (2) Feng–Linetsky method based on Hilbert t...
متن کاملConnecting discrete and continuous path-dependent options
This paper develops methods for relating the prices of discreteand continuous-time versions of path-dependent options sensitive to extremal values of the underlying asset, including lookback, barrier, and hindsight options. The relationships take the form of correction terms that can be interpreted as shifting a barrier, a strike, or an extremal price. These correction terms enable us to use cl...
متن کاملOn the Valuation of Fader and Discrete Barrier Options in Heston's Stochastic Volatility Model
We focus on closed-form option pricing in Heston’s stochastic volatility model, where closed-form formulas exist only for a few option types. Most of these closed-form solutions are constructed from characteristic functions. We follow this closed-form approach and derive multivariate characteristic functions depending on at least two spot values for different points in time. The derived charact...
متن کاملOn Pricing Barrier Options with Discrete Monitoring
This paper proposes a new approximation method for pricing barrier options with discrete monitoring under stochastic volatility environment. In particular, the integration-by-parts formula and the duality formula in Malliavin calculus are effectively applied in an asymptotic expansion approach. First, the paper derives an asymptotic expansion for generalized Wiener functionals. After it is appl...
متن کاملNumerical algorithm for discrete barrier option pricing in a Black-Scholes model with stationary process
In this article, we propose a numerical algorithm for computing price of discrete single and double barrier option under the emph{Black-Scholes} model. In virtue of some general transformations, the partial differential equations of option pricing in different monitoring dates are converted into simple diffusion equations. The present method is fast compared to alterna...
متن کامل