Search results with tag "Geometric brownian motion"
Introduction to Probability Models
www.ctanujit.org10. Brownian Motion and Stationary Processes 625 10.1. Brownian Motion 625 10.2. Hitting Times, Maximum Variable, and the Gambler’s Ruin Problem 629 10.3. Variations on Brownian Motion 631 10.3.1. Brownian Motion with Drift 631 10.3.2. Geometric Brownian Motion 631 10.4. Pricing Stock Options 632 10.4.1. An Example in Options Pricing 632 10.4.2.
1 Geometric Brownian motion - Columbia
www.columbia.edu1.5 The Binomial model as an approximation to geometric BM The binomial lattice model (BLM) that we used earlier is in fact an approximation to geometric BM, and we proceed here to explain the details. Recall that for BLM, S n = S 0Y 1Y 2 ···Y n, n ≥ 0 where the Y i are i.i.d. r.v.s. distributed as P(Y = u) = p, P(Y = d) = 1−p. Besides ...
Lecture #28: Calculations with Itoˆ’s Formula
stat.math.uregina.cafollows geometric Brownian motion with drift 0.05 and volatility 0.3 so that it satisfies the stochastic di↵erential equation dXt =0.3Xt dBt +0.05Xt dt. If the price of the stock at time 2 is 30, determine the probability that the price of the stock at time 2.5 is between 30 and 33. Solution.
Black-Scholes Equations
www.math.cuhk.edu.hk82 MAT4210 Notes by R. Chan i) The asset price follows the geometric Brownian motion discussed in Chapter 6. That is, dS(t) = µS(t)dt+σS(t)dX(t). (1) ii) The risk-free interest rate r and the asset volatility σ are known functions. iii) There are no transaction costs.