Hi Anyone has ideas of hedging a book with jump diffusion model?I have calibrated the Merton model to a emergent ccy option market, and use the numerical method with resulting parameters to pricing exotic option. However I'm not sure with the meanings of the exotic price I got from Merton model.They seems to be much lower than theoretic value. For example, a 50% one touch option may be 38% in Merton model.The parameters I got wewe sigma(vol of underlying) , lamda(jump intensity), delta (vol of jump), mu( mean of jump). Please kinldly advise how to use Merton model in practice?

QuoteOriginally posted by: dinnerHi For example, a 50% one touch option may be 38% in Merton model.What does that sentence mean?Also, what was the numerical method?regards,

Hi Alan,Thanks for your reply.Frist I calibrate Merton model to PV market and got four parameters. then I use them to price exotic option, say one touch.However I found that it seems the resulting price tends to be lower than theoretic value. For example , if I price a one touch with TV = 50% , then the resulting merton price may be 38%, which is much lower than TV.

Some possibilities:1. Everything is ok, the lower one-touch is because the distributionhas mass distributed differently than log-normal. What do you get if you put the one-touch barrier the same log-return 'distance' below the stock price? (assuming the orig. was above.)2. Your numerical method for computing the one-touch price was wrong.For comments, you'll have to explain your method in some detail.3. Your calibration was wrong.To check, perhaps you should compare the vanilla call prices where thestrike is at the one-touch barrier. How do these two prices compare under the twomodels? What exactly are all the parameter values?Finally, when you say the TV is 50%, I assume you mean under the Black-Scholesassumptions, but with what volatility? (not what numerical value, but howdo you get that single volatility?). regards,

QuoteOriginally posted by: dinnerHi Anyone has ideas of hedging a book with jump diffusion model?What instruments are available? Is it only risk free and underlying or can you use options as well to hedge (i.e. the ones you used to extract the risk neutral parameters)?Kyriakos

This might be useful for you. http://www.cs.uwaterloo.ca/~paforsyt/jump_hedge.pdf

It is true that jump+diffusion tends to undervalue OT (vs. market), the reason is that the diffusive vol gets too low after calibration to vanilla market. Although the model has 4 parameters, it is has effectively 3 parameters (say fix lambda and calibrate to atm, bf and rr , i.e. get diffusive vol, mean jump and st.dev. of jumps; change lambda, say twice higher, and re-calibrate and you get that the diffusive vol hardly changed and the value of OT hardly changed (on any reasonable scale) ). Pure stoch vol tends to overvalue emerging market's OT (when calibrated to vanilla market) when TV is not high. One conclusion is that the spot dynamics does have jumps but one needs to make the parameters (at least vol & lambda) stochastic (or even having jumps in them too). TV = BS value at vol = ATM.

Use at least a jump-diffusion model that not assumes all jumps are non-systematic; Bates 1991 is a good start. And then I am sure Alan has some great jump-diffusion models up his sleeve, potentially even combined with stochastic vol

Hi It's that means that the single jump + diffusion may not be sufficient to explain the market price ? If that's the case, can someone kinldy suggest any materials or topics to study?My purpose is to catch the market price of emergent ccys option (KRW/TWD/MYR.....). So any suggestion on this topic will be highly appreciated.Hi CollectorIs the paper u noted Bates's "Jump and stochatic volatility: the exchange rate process implicit in Deutschemark"?Thanks a lot.

Bates, D. S. (1991): “The Crash of ’87: Was It Expected? The Evidence from Options Markets,” Journal of Finance, 46(3), 1009–1044''more generalized jump-diffusion model than Merton-76 for example it do not assume all jumps are unsystematic, but more realistic systematic.To hedge systematic jumps in option portfolio you naturally have to use other options as mentioned by Bates, this is much closer to what knowledgeable market makers and option traders actually do, my forthcoming Know Your Weapon Part 3 also discusses this in much more detail, but you have to wait to fall to get hold of it becaue I am working on it just now, and not sure if I should publish it, too many secrets ,it is not so much about jump-diffusion models more about what option traders do and not should do, but several pages discussion on jumps, jumps are alfa omega