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January 19th, 2015, 1:23 am
Forum: Numerical Methods Forum
Topic: How to calibrate stochastic model with time series?
Replies: 4
Views: 4860

### How to calibrate stochastic model with time series?

<t>How to calibrate stochastic model with time series? I know there are lots of numerical methods like solving Fokker-Planck PDE, Disrete maximum likelihood, Hermite polynomial expansion, Markov Chain Monte Carlo. But is there any availble numerical library to do this? I prefer open source library. ...
January 15th, 2015, 4:59 am
Forum: Student Forum
Topic: How to derive Hamilton-Jacobi-Bellman Equation from supreme of expectation?
Replies: 3
Views: 3314

### How to derive Hamilton-Jacobi-Bellman Equation from supreme of expectation?

<t>Thank you, Alan. I know what you mean. I agree that Equation (2) can be derived from g(t, Vt, Xt)=sup[E( g(T, VT, XT) ) ].But I am still not sure how to get g(t, Vt, Xt) from Equation (1). There is an exponetial function and a parameter alpha in Equation (1), which finally disppear in Equaiton (2...
January 14th, 2015, 9:32 am
Forum: Student Forum
Topic: How to derive Hamilton-Jacobi-Bellman Equation from supreme of expectation?
Replies: 3
Views: 3314

### How to derive Hamilton-Jacobi-Bellman Equation from supreme of expectation?

thanks
January 14th, 2015, 12:46 am
Forum: Student Forum
Topic: A quick question on Ito's integral
Replies: 8
Views: 3722

### A quick question on Ito's integral

Thank you Alan. I completely agree with you
January 12th, 2015, 3:03 pm
Forum: Student Forum
Topic: A quick question on Ito's integral
Replies: 8
Views: 3722

### A quick question on Ito's integral

<t>The above solution uses a simple method to calculate It-Is.Although the result looks quite correct to me, the process seems to have some problem. The last equation omit lots of terms. After t1, there should be more terms t2, t3... until t. If we write out the long series (rather than just 3 terms...
January 5th, 2015, 7:51 am
Forum: General Forum
Topic: How to forecast volatility based on fundamental analysis?
Replies: 1
Views: 3215

### How to forecast volatility based on fundamental analysis?

<t>I know there are lots of papers and books cover forecasting volatility by quantitative model. However, is there any practical guide on forecast volatility based on fundamental analysis, like the analysis on government policy, economic conditions of foreign/domestic countries, customers' demand an...
December 31st, 2014, 8:10 am
Forum: Student Forum
Topic: 2D martingale problem
Replies: 5
Views: 3545

### 2D martingale problem

Thank you Alan. I have sth to pick up.
December 29th, 2014, 1:32 am
Forum: Student Forum
Topic: 2D martingale problem
Replies: 5
Views: 3545

### 2D martingale problem

Is there anything unclear on this question? The interviewer suggested a martingale be constructed in 2D to solve this problem, but I really cannot figure it out. Any further suggestions from you guys?
December 27th, 2014, 9:30 am
Forum: Student Forum
Topic: 2D martingale problem
Replies: 5
Views: 3545

### 2D martingale problem

<t>This is an interview question. Circle A with radius a is inside Circle B with radius b. a 2D independent Brownian motion start from point M with distance r to center of circle A. point M locates between circle A and cirlce B. What's the probability of reaching circle A before reaching circle B? <...
December 24th, 2014, 12:11 am
Forum: Numerical Methods Forum
Topic: Why pricing American option by free-boundary method and MC?
Replies: 5
Views: 4646

### Why pricing American option by free-boundary method and MC?

<t>Thank you, Cuchulainn.The finite difference scheme I use is Crank?Nicolson, which is second order accuracy. Do you mean assigning payoff to option price directly would make the accuracy order to 1? If so, can a classical 4th order Runge-Kutta can cure this disadvantage, where I can assign payoff ...
December 23rd, 2014, 3:10 pm
Forum: General Forum
Topic: Expectation of volatility or sqrt(expectation of variance)?
Replies: 6
Views: 3793

### Expectation of volatility or sqrt(expectation of variance)?

Thank you for your suggestions Alan.
December 23rd, 2014, 3:07 pm
Forum: Numerical Methods Forum
Topic: Why pricing American option by free-boundary method and MC?
Replies: 5
Views: 4646

### Why pricing American option by free-boundary method and MC?

<t>As I know, American-type option can be solved by PDE method. When the PDE is integrated backward, the option price can be simply assigned by option payoff at this time step if the payoff is bigger. This method seems work well for me, but is there any disadvantage of this method? Otherwise why do ...
December 23rd, 2014, 11:22 am
Topic: How to allocate asset in pairs trading after getting cointegration?
Replies: 0
Views: 3537

### How to allocate asset in pairs trading after getting cointegration?

<t>In Carol Alexander?s book, Market Models, page 370, it says, "Suppose a benchmark and log price y is to be tracked with a number of assets with log prices x1,x2,..,xn. The Engle-Granger cointegration method is to regress y on a constant and x1,x2,..,xn, and then to test the residuals for stationa...
December 23rd, 2014, 3:22 am
Forum: General Forum
Topic: Expectation of volatility or sqrt(expectation of variance)?
Replies: 6
Views: 3793

### Expectation of volatility or sqrt(expectation of variance)?

<t>Thank you, Alan. MC is a powerful way to resolve this problem.I have tried MC to simulate discrete hedging PnL, where underlying price is generated in the following way:d(Var)=kappa*(theta-Var)*dt+gamma*Var*dZsigma=sqrt(Var)dS=r*S*dt+sigma*S*dWHere Var is the variance and sigma is the volatility....
December 22nd, 2014, 2:28 pm
Forum: General Forum
Topic: Expectation of volatility or sqrt(expectation of variance)?
Replies: 6
Views: 3793

### Expectation of volatility or sqrt(expectation of variance)?

<t>Thank you for your suggestion, Alan.I haven't tried this. However, I guess the "mean loss" should depend on the strike, expiration, etc.. In practice, we may also need to consider the "standard deviation of loss". It may also depend on case by case, I guess. I am interested to know if there is an...
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