ステイス アントニー

Abstract
In this paper we develop a method to find the price of several options whose payoff depends on a volume weighted average price (VWAP). Fixed and floating strike VWAP, together with digital VWAP contracts are considered. Throughout we assume that the stock follows a geometric Brownian motion and the rate of trades evolves as a mean reverting process. It is assumed that the VWAP at the final time has a lognormal distribution. The parameters of the approximating lognormal distribution… さらに表示

Abstract
In this paper we develop a method to find the price of several options whose payoff depends on a volume weighted average price (VWAP). Fixed and floating strike VWAP, together with digital VWAP contracts are considered. Throughout we assume that the stock follows a geometric Brownian motion and the rate of trades evolves as a mean reverting process. It is assumed that the VWAP at the final time has a lognormal distribution. The parameters of the approximating lognormal distribution are obtained by matching the first two moments of the volume weighted average price with a lognormal process. A price is then obtained for the fixed strike and digital options when the market price of risk is a constant. We concentrate on the price for calls, prices for puts can be obtained in an analogous manner. 部分表示

This is part of the abstract. Full abstract at the link.
In this work, we developed methods to price both fixed and floating strike Volume Weighted Average Price (VWAP) options. VWAP options have a payoff that is dependent on both the stock price and volume of stock traded over the lifetime of the option. We concentrate on the valuation of European style, fixed and floating strike call options. Little additional effort is required to adapt the results of this work to value puts. First… さらに表示

This is part of the abstract. Full abstract at the link.
In this work, we developed methods to price both fixed and floating strike Volume Weighted Average Price (VWAP) options. VWAP options have a payoff that is dependent on both the stock price and volume of stock traded over the lifetime of the option. We concentrate on the valuation of European style, fixed and floating strike call options. Little additional effort is required to adapt the results of this work to value puts. First, introductory mathematical material is presented, followed by a general overview of options and how they are priced. The VWAP is then formally introduced, and some examples of VWAP options in practice are given. Expectations and a partial differential equation that describes the price of the options are then constructed. Throughout, we assume the stock price evolves as a geometric Brownian motion process, and the volume is a fast mean reverting process. Upper and lower bounds are established for the price of both fixed and floating strike VWAP options. These bounds are given as analytic formulae and are independent of the volume model. The bounds are obtained from a simple put-call type parity. We then interpret these bounds further. The upper bounds represent the minimum cost of hedging all of the risk. A Monte Carlo investigation is then performed; this gives a vivid picture of how the VWAP options behave. It also allows later results to be benchmarked. In addition to vanilla Monte Carlo, some effective controls variates are found. We conclude the Monte Carlo investigation by finding the Greeks by the finite difference, pathwise, and likelihood methods. Next, approximations to the prices of the VWAP options are obtained by matching the first two moments of the VWAP to a lognormal distribution. For the fixed strike, a partial differential equation similar to the Black-Scholes-Merton one is obtained. 部分表示

MATLAB is a sophisticated software tool for numerical analysis and visualization. The University of Queensland has adopted Matlab as its official teaching package across large first year mathematics courses. In the past, the package has met severe resistance from students who have not appreciated their computational experience. Several main factors contribute: first, the software is numerical rather than symbolic, providing a departure from the thinking patterns presented in lectures and… さらに表示

MATLAB is a sophisticated software tool for numerical analysis and visualization. The University of Queensland has adopted Matlab as its official teaching package across large first year mathematics courses. In the past, the package has met severe resistance from students who have not appreciated their computational experience. Several main factors contribute: first, the software is numerical rather than symbolic, providing a departure from the thinking patterns presented in lectures and tutorials. Second, many students cannot see a direct connection between the laboratory exercises and core course material from lectures. Third, the students find hurdles to entry as commands often return incomprehensible error messages and don’t execute, and programs are difficult to write and debug. Overall, the details of the mathematics are lost in trying to negotiate the software. After considerable effort in tuning, it appears that a sequence of innovations has captured student support and added considerable value to both the computational and traditional learning process. 部分表示