SERVING THE QUANTITATIVE FINANCE COMMUNITY

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September 8th, 2015, 12:00 pm
Forum: Student Forum
Topic: How to hedge exotic interest rate derivative under BGM model?
Replies: 3
Views: 2468

### How to hedge exotic interest rate derivative under BGM model?

<t>In M.S. Joshi ?s book ?The concepts of mathematical finance?, it talks a lot on pricing exotic interest rate derivative under BGM model. I think it is mainly based on the Monte Carlo method by simulating the forward rate. However, I am not clear on how to hedge the exotic interest rate derivative...
June 29th, 2015, 12:57 am
Forum: General Forum
Topic: Is there any practical method to replicate stock index option by index future?
Replies: 1
Views: 2887

### Is there any practical method to replicate stock index option by index future?

<t>Suppose the option is on stock index. Since it is difficult to buy or sell stock index, index future is preferred for hedging the option. However, there are some different factors between index future an stock index. For example:1. Volatility. Future?s volatility is usually larger than stock inde...
June 18th, 2015, 3:18 pm
Forum: Student Forum
Topic: How to price this option?
Replies: 7
Views: 3052

### How to price this option?

<t>I mean you can exercise as soon as it hits the barrier 100.If I receive option fee 0.7, and buy 0.01 shares of the underlying at 70, when it researches 100, I can make a profit of 0.3. This profit plus the option fee is equal to the option payoff 1. The payoff of this option is 1 once it hits 100...
June 18th, 2015, 12:58 pm
Forum: Student Forum
Topic: How to price this option?
Replies: 7
Views: 3052

### How to price this option?

<t>Suppose the underlying now is 70, once itreaches 100, the option?s pay off is 1. This option never expires and assumesinterest rate is 0.I think one can hedge this option byholding 0.01 share of this underlying, once it reaches 100, then earn (100-70)*0.01=0.3.So the price of this option should b...
March 25th, 2015, 1:08 am
Forum: General Forum
Topic: How to interpret the correlation from Heston model calibration?
Replies: 9
Views: 4022

### How to interpret the correlation from Heston model calibration?

<t>Thank you Alan. The method in white paper "The CBOE Volatility Index - VIX"generate a better result on BS implied vol. It's not a very smooth curve, but I can see some oscillations of volatility between 25% and 27% for options with long expiration days.1.However, I can not understand well the log...
March 24th, 2015, 10:45 am
Forum: General Forum
Topic: How to interpret the correlation from Heston model calibration?
Replies: 9
Views: 4022

### 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....
March 23rd, 2015, 12:26 am
Forum: General Forum
Topic: How to interpret the correlation from Heston model calibration?
Replies: 9
Views: 4022

### 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...
March 20th, 2015, 8:17 am
Forum: General Forum
Topic: How to interpret the correlation from Heston model calibration?
Replies: 9
Views: 4022

### 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 ...
March 19th, 2015, 3:05 pm
Forum: General Forum
Topic: How to price European put option with short selling cost?
Replies: 2
Views: 3032

### 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...
March 18th, 2015, 2:47 pm
Forum: General Forum
Topic: How to price European put option with short selling cost?
Replies: 2
Views: 3032

### 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...
March 10th, 2015, 8:10 am
Topic: Comparison between Heston models calibrated by historical time series and instant option prices.
Replies: 3
Views: 4362

### 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...
March 6th, 2015, 4:33 am
Topic: Comparison between Heston models calibrated by historical time series and instant option prices.
Replies: 3
Views: 4362

### 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...
January 29th, 2015, 5:27 am
Forum: Numerical Methods Forum
Topic: Is HJB equation a local or global optimum?
Replies: 1
Views: 4689

### 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...
January 21st, 2015, 1:11 am
Forum: Numerical Methods Forum
Topic: How to calibrate stochastic model with time series?
Replies: 4
Views: 4835

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

Thanks a lot, Alan
January 20th, 2015, 1:34 am
Forum: Numerical Methods Forum
Topic: How to calibrate stochastic model with time series?
Replies: 4
Views: 4835

### 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...
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