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by EdisonCruise
March 24th, 2015, 10:45 am
Forum: General Forum
Topic: How to interpret the correlation from Heston model calibration?
Replies: 9
Views: 3806

How to interpret the correlation from Heston model calibration?

<t>Thank you all for your suggestions.The short sell rate is indeed very high, roughly 8% p.a. in this market. May I know if there is any industrial standard method to calculate implied volatility in such a case?If no, is there any problem if I do the following?Still assume the put-cal parity holds....
by EdisonCruise
March 23rd, 2015, 12:26 am
Forum: General Forum
Topic: How to interpret the correlation from Heston model calibration?
Replies: 9
Views: 3806

How to interpret the correlation from Heston model calibration?

<t>Thank you Alan.The underlying is an ETF mutual fund in a developing country.The BS implied vols for call option are not smooth even only OTM options are included. The BS implied vols for put option are just going down from low strike to high strike, which is much "smoother". There are great diffe...
by EdisonCruise
March 20th, 2015, 8:17 am
Forum: General Forum
Topic: How to interpret the correlation from Heston model calibration?
Replies: 9
Views: 3806

How to interpret the correlation from Heston model calibration?

<t>Heston model can be calibrated by call and put option market data separately. The correlation from call option is very close to 1, while the one from put option is very close to -1. Does it mean people trading call option anticipate volatility goes up, when market goes up; and people trading put ...
by EdisonCruise
March 19th, 2015, 3:05 pm
Forum: General Forum
Topic: How to price European put option with short selling cost?
Replies: 2
Views: 2938

How to price European put option with short selling cost?

<t>Thank you for your reply. The assumption here is the situation in practice, where no repo can receive in the long stock position. The market is not liquid. Some policy imposes a restriction on borrowing stock by a high short selling rate. So I doubt if there is a put-call parity in this case, whi...
by EdisonCruise
March 18th, 2015, 2:47 pm
Forum: General Forum
Topic: How to price European put option with short selling cost?
Replies: 2
Views: 2938

How to price European put option with short selling cost?

<t>One sells a European put option and wants to hedge it by short selling the stock. If he does not own any stock, then he need to borrow it at a high rate L, say 10% p.a. from the borrower. He cannot get any money from short selling, which is different from the BS assumption. How to price this Euro...
by EdisonCruise
March 10th, 2015, 8:10 am
Forum: Trading Forum
Topic: Comparison between Heston models calibrated by historical time series and instant option prices.
Replies: 3
Views: 4238

Comparison between Heston models calibrated by historical time series and instant option prices.

<t>Thank you Alan. Trading the difference between OTM option's vol and historical vol (caluclated by annualized standard deviation) is indeed on risk premium.Howevver, if one calibrate Heston model by historical data, then he should also be able to get a "vol surface" as the implied vol calibrated f...
by EdisonCruise
March 6th, 2015, 4:33 am
Forum: Trading Forum
Topic: Comparison between Heston models calibrated by historical time series and instant option prices.
Replies: 3
Views: 4238

Comparison between Heston models calibrated by historical time series and instant option prices.

<t>Is it possible to make a volatility trading strategy like this: (1) Use SP500 historical time series to calibrate Heston model, then calculate the expected realized volatility v1 in the period T.(2) Use SP500 option prices to calibrate Heston model, then calculate the expected realized volatility...
by EdisonCruise
January 29th, 2015, 5:27 am
Forum: Numerical Methods Forum
Topic: Is HJB equation a local or global optimum?
Replies: 1
Views: 4594

Is HJB equation a local or global optimum?

<r>I am a bit confused on the HJB equation. In the derivation of Hamilton?Jacobi?Bellman (HJB) equation, we take the first order optimality at each time step, so that the trading strategy is optimum over the next infinitesimal time step. It seems that this strategy gives only local optimum, which is...
by EdisonCruise
January 20th, 2015, 1:34 am
Forum: Numerical Methods Forum
Topic: How to calibrate stochastic model with time series?
Replies: 4
Views: 4681

How to calibrate stochastic model with time series?

<t>Thanks again, Alan. I want to use maximum likelihood, but I am not sure how to construct the likelihood function for specific stochastic models, especially high dimensional models. I think mathematica, matlab only provide optimizaiton functions, rather than likelihood function. Are there any good...
by EdisonCruise
January 19th, 2015, 1:23 am
Forum: Numerical Methods Forum
Topic: How to calibrate stochastic model with time series?
Replies: 4
Views: 4681

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. ...
by EdisonCruise
January 15th, 2015, 4:59 am
Forum: Student Forum
Topic: How to derive Hamilton-Jacobi-Bellman Equation from supreme of expectation?
Replies: 3
Views: 3177

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...
by EdisonCruise
January 14th, 2015, 12:46 am
Forum: Student Forum
Topic: A quick question on Ito's integral
Replies: 8
Views: 3545

A quick question on Ito's integral

Thank you Alan. I completely agree with you
by EdisonCruise
January 12th, 2015, 3:03 pm
Forum: Student Forum
Topic: A quick question on Ito's integral
Replies: 8
Views: 3545

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...
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