• C++ Programming for Financial Engineering
    Highly recommended by thousands of MFE students. Covers essential C++ topics with applications to financial engineering. Learn more Join!
    Python for Finance with Intro to Data Science
    Gain practical understanding of Python to read, understand, and write professional Python code for your first day on the job. Learn more Join!
    An Intuition-Based Options Primer for FE
    Ideal for entry level positions interviews and graduate studies, specializing in options trading arbitrage and options valuation models. Learn more Join!

Hedge Needs - Which Model is Best to use?

Joined
6/11/10
Messages
189
Points
28
Suppose you need to hedge an exotic option without any frequently traded vanilla option as means, and all you have is a money account and stock, then which model would you choose - simple Black-Scholes, CEV modification, Hull White or Heston Stochastic Volatility type, or Jump Diffusion?

I came across many textbooks, but the models' goal seems to explain the volatility surface in the market. However, a real hedger's goal is to beat the market or produce something not exist in the market, otherwise why hedge?
 
I think you confuse the goal of the hedger with the goal of an arbitrageur. The hedger wants to offset potential losses/gains that come up from his original business/deal/whatever.
 
I think you confuse the goal of the hedger with the goal of an arbitrageur. The hedger wants to offset potential losses/gains that come up from his original business/deal/whatever.

So do you know which model is best for hedging purpose?
 
You're already fighting a losing battle trying to hedge an exotic without recourse to vanillas. You cannot hedge factors that aren't traded.
 
You're already fighting a losing battle trying to hedge an exotic without recourse to vanillas. You cannot hedge factors that aren't traded.
So basically I can only use Black-Scholes or CEV to hedge them?
 
This is a bit of a difficult question because your choice of model depends a lot on how you believe surface dynamics evolve over the course of the hedging of the option, which in turn implies you are hedging a lot of things other than delta. If you are restricting yourself to only hedging the delta of the option, none of these models will give you a satisfactory hedging strategy, as the deltas they will tell you to hedge assume you will also rebalance your vanilla hedges as the market moves around. I suppose what you might do is a statistical analysis of what happens to vol and the surface when the underlying moves one way or the other, and hedge the delta that analysis comes up with. I'm not a massive fan of that strategy, and it won't hedge a lot of scenarios (most obviously static decay), but I'm not a fan of trying to hedge exotic options with only delta either. What kind of option are we talking about anyway?
 
This is a bit of a difficult question because your choice of model depends a lot on how you believe surface dynamics evolve over the course of the hedging of the option, which in turn implies you are hedging a lot of things other than delta. If you are restricting yourself to only hedging the delta of the option, none of these models will give you a satisfactory hedging strategy, as the deltas they will tell you to hedge assume you will also rebalance your vanilla hedges as the market moves around. I suppose what you might do is a statistical analysis of what happens to vol and the surface when the underlying moves one way or the other, and hedge the delta that analysis comes up with. I'm not a massive fan of that strategy, and it won't hedge a lot of scenarios (most obviously static decay), but I'm not a fan of trying to hedge exotic options with only delta either. What kind of option are we talking about anyway?
I am in a very immature market where even vanilla options are in scarce. To simplify the question, just hedge an European Call on a stock, which is the best?
 
I have heard the rumor that option shall be hedged according to recent volatility. So I guess a SV model outperforms a BS?
 
I have heard the rumor that option shall be hedged according to recent volatility. So I guess a SV model outperforms a BS?
However someone told me that SV model is not complete, so forget about it and just stick to BS.
 
If you have no idea where the smile is and don't plan on hedging your vol exposure ever, I suppose just use Black Scholes, but this smells like a bad idea. What are you trying to accomplish?
 
If you have no idea where the smile is and don't plan on hedging your vol exposure ever, I suppose just use Black Scholes, but this smells like a bad idea. What are you trying to accomplish?

I know the real stock price distribution has thick tails, so traditional BS method may encounter unexpected loss and may cost a lot. I want to hedge an option as smooth and cheap as possible. After all, if I underwrite an option, my profit is premium revenue minus hedging cost. If I have to choose between cost stability and average cost of hedging, I choose stability, or minimal variance. After all, it is hard to promote an option in such an immature market, so I wanna hedge well for a deal with just underlying stock and money account .
 
If you have no idea where the smile is and don't plan on hedging your vol exposure ever, I suppose just use Black Scholes, but this smells like a bad idea. What are you trying to accomplish?
Any suggestion?:)
 
Any suggestion?:)

i like two-factor lognormal stoch vol with jumps. "immature market" does it mean there is no bid if SPX craters 100 points? what market are you looking at?


If you have no idea where the smile is and don't plan on hedging your vol exposure ever, I suppose just use Black Scholes, but this smells like a bad idea. What are you trying to accomplish?

i think his trying to make a shipload of money
 
i like two-factor lognormal stoch vol with jumps. "immature market" does it mean there is no bid if SPX craters 100 points? what market are you looking at?

The market consisting of only the OTC market - each option underwriter retails their options to clients by contract.
 
Last edited:
for empirical option pricing check out Bouchaud's "Theory of financial risk". good book and has a chapter on "hedged MC". i think its a gd starting point. i have implemented it, and it works.
 
If you're only trading vanillas and have a decent measure of the distribution, try pricing using the p-measure expectation just by integrating over the probability distribution (this is the important piece, not so much the hedging), and hedging using standard BS.

SV models are for pricing exotics; vanillas are only sensitive to the probability distribution (ie not path dependent).
 
If you're only trading vanillas and have a decent measure of the distribution, try pricing using the p-measure expectation just by integrating over the probability distribution (this is the important piece, not so much the hedging), and hedging using standard BS.

SV models are for pricing exotics; vanillas are only sensitive to the probability distribution (ie not path dependent).

That sounds like that I go back to the times before Black-Scholes...
 
That sounds like that I go back to the times before Black-Scholes...

I see your post quite many years ago. But did you come out with a good solution about this? I think I am having same situation with you. Exotic options on OTC, immature markets without vanilla, straight to the point, only account money and stocks.
 
Back
Top