By James A. Primbs
This booklet offers the quickest and least difficult path to the vast majority of the implications and equations in by-product pricing, and offers the reader the instruments essential to expand those principles to new events that they could stumble upon. It does so by means of concentrating on a unmarried underlying precept that's effortless to know, after which it indicates that this precept is the most important to the vast majority of the consequences in by-product pricing. In that feel, it offers the "big photo" of spinoff pricing through concentrating on the underlying precept and never on mathematical technicalities. After examining this ebook, one is provided with the instruments had to expand the strategies to any new pricing scenario.
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Additional info for A Factor Model Approach to Derivative Pricing
1 Jump Diffusion as a Stock Price Model When used as the model for a stock price S(t), the jump diffusion process leads to the stock’s instantaneous return being r= dS = adt + bdz + (Y − 1)dπ, S− which is the sum of three parts. The term adt is a deterministic drift, bdz is a Gaussian term, and finally (Y − 1)dπ allows random jumps to occur which could represent sudden unexpected events such as earnings surprises or the like. 20) where a, b, c, and f are constants. We will obtain the solution to this stochastic differential equation using the concept of an integrating factor that arises in ordinary differential equations .
P. p. 1) has a mean and variance that agree with a Poisson random variable with parameter αdt to order dt. 4 Poisson Processes. Consider the time interval [0, 1]. Chop this time interval into n parts of equal length. p. p. 1 − α/n. 2) n Xi . 3) i=1 Answer the following, where P(·) denotes probability. (a) What is P(Y = 0)? (b) In your answer in (a), take the limit as n → ∞. What do you get? (b) What is P(Y = 1)? (c) Again take the limit. What is your answer? (d) Now consider an arbitrary but fixed k with k < n.
Which term has standard deviation of lowest order in dt? 7). 31). CHAPTER 3 Stochastic Differential Equations with Solutions n this chapter, we review some stochastic differential equations that have closed form solutions. These are also some of the stochastic differential equations used for modeling asset prices and other relevant financial variables. In these solutions, note the role that Ito’s lemma plays. Most importantly, not many stochastic differential equations have closed form solutions.
A Factor Model Approach to Derivative Pricing by James A. Primbs