Using a change of time variable, reduce to the diffusion equation when c( ) 0 Consider the BlackScholes equation, when and r can be functions of time, but k 2r 2 is still a constant Reduce the BlackScholes equation to the diffusion equation in this case a2u du c(t) at ax2

Question: Using a change of time variable, reduce to the diffusion equation when c( ) > 0. Consider the BlackScholes equation, when and r can

Using a change of time variable, reduce

a2u du c(t)- at ax2 *

to the diffusion equation when c(τ ) > 0.
Consider the Black–Scholes equation, when σ and r can be functions of time, but k = 2r/σ² is still a constant. Reduce the Black–Scholes equation to the diffusion equation in this case.

a2u du c(t)- at ax2 *

Step by Step Solution

★★★★★

3.51 Rating (168 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Answer 1 The reduced equation ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Introduces Quantitative Finance Questions!

The diffusion equation is valid when many elementary steps are taken in the time interval of interest, but the random walk calculation lets us discuss distributions for short times as well as for...

The homogeneous diffusion equation (5.160) for the vector potential for quasi-static fields in unbounded conducting media has a solution to the initial value problem ?of the form, A(x, t) = ? d 3 x'...

Using Equations (9-14) and (9-7), develop Equation (9-26). Equation (9-14) Equation (9-7) Equation (9-26) 4I Co 1.47 1/3 for Re1800

Partial Differential Equations The Black-Scholes-Merton (BSM or just BS) PDE for the value Ct, S) of a derivative security as a function of time t and underlying asset price level S(t) = S takes the...

A seismic probe bores itself into the seabed, going as deep as it can before running out of fuel. This takes about five minutes. It rotates its spiral drill head at rate R(t) that follows a...

10 Green's functions for PDEs In this final chapter we will apply the idea of Green's functions to PDEs, enabling us to solve the wave equation, diffusion equation and Laplace equation in unbounded...

SEE "DOCUMENT 1" FOR CRITERIA 2 "DOCUMENT 2" FOR CRITERIA 4 You are to write a 3 to 4 page paper following APA rules for the title page, citations and appropriate references within the body of the...

SEE "DOCUMENT 1" FOR CRITERIA 2 "DOCUMENT 2" FOR CRITERIA 4. You are to write a 2 to 4 page paper following APA rules for the title page, citations and appropriate references within the body of the...

Jasper is single and is a computer software consultant with a college degree. He feels that one of the reasons for his success is that he continually updates his knowledge by taking classes at the...

Reconsider the model in Prob. 4.1-5. Interpret the right-hand side of the respective functional constraints as the amount available of the respective resources. (a) Use graphical analysis as in Fig....

Jan, a business owner, sold a piece of equipment for $10,000 and no assets remain in its class. Jan's UCC balance was $13,000 and the capital cost of the equipment sold was $16,000. This transaction...

3. Are there other areas of assessment that should be considered?

Let $f(\theta)$ be the $2 \pi$-periodic function determined by the formula \[f(\theta)=\theta^{2}, \quad \text { for }-\pi \leq \theta \leq \pi\] Find the Fourier series for $f(\theta)$.

Consider the signal $f(t)=\sin (7 t)$. Use Matlab to obtain the discrete wavelets transform of this signal.

Consider the periodic signal \[f(t)=\left\{\begin{array}{lr}\cos (t)+D, & -1 \leq t \leq 0 \\\sin \left(t^{6} ight) / t^{3}, & 0 \leq t\leq 2\end{array} ight.\] where \(D=\sin \left(2^{6} ight) /...

Time spent using e-mail per session is normally distributed, with u = 8 minutes and o = 2 minutes. If you select a random sample of 25 sessions, a. what is the probability that the sample mean is...

Bottoms Up Diaper Service is considering the purchase of a new industrial washer. It can purchase the washer for $6,300 and sell its old washer for $2,100. The new washer will last for 6 years and...

Samson Company had the following transactions. 1. Issued 5,000 shares of $100 par preferred stock at $107 for cash. 2. Issued 8,000 share of common stock with a par value of $10 for $120,000. 3....