- TitanPartners
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I take your point TinMan. It would be interesting to try to bring in some new ideas to derivatives contract valuation using a wider variety of applied maths ... perhaps cure my math-finance-cynicism :-)Paul: Haha, is the only way forward to buy your book then ;-)Are there any freely available papers we can look at with an overview of this type of task rather than just specifics?

QuoteOriginally posted by: BramJQuoteOriginally posted by: frenchXI agree with Tinman that we could talk for weeks what we need is a quantitative comparison. I also distinguish a model for pricing to a model for hedging. Just to threadjack slightly: I might misunderstand, so what do you mean by that? Having different stochastic models for the behaviour of the underlying for pricing and hedging? Suppose your pricing model gives a value P (or a range (P1,P2) for my question I am not looking to get into discussions about points versus ranges of values) and your hedging model gives a price of H. I'd say you either have P close to H and then your hedging model is a good pricing model or you have P and H very differently. In the latter case, how are you going to get the distribution of the replicated payoff centered around P instead of H?Edit: obviously P and H could be close initially but could expect one of them to be more misspecified as the other and hence one of the values be more stable as the other. But then why not price and hedge on the more stable/robust model?When I say a difference between the pricing model and the hedging one I didn't mean in that sense but let me develop a bit The best will be to use an example.What I believe in is a combination of S(VM)² and UVM. Basically is a bit like fusionning SV and UVM. You will have a best case/worst case for the mean and the variance. You can imagine the worst value being mean_worst-eps*worst_variance and the best one being mean_best+eps*best_variance. Delta is choosen for each to cancel the directional risk and to minimize the variance. Then you built a static hedge to reduce your spread between best case/ worst case. Once you have that, you sell your exotic to your reduce best case (seller case) or you can buy it for your reduced worst case (buyer side). To agree with the market you can play a bit with eps (your risk aversion) to evaluate your loss.Once you have sell your exotic, you have to hedge it. Hedging can only be done discretely at one cost. The hedging model is very similar to the pricing one except that there is no continuous delta hedging. The underlying is seen as a call option with 0 strike and is incorporated in the semi static hedging. Being mark to market, this static hedging includes transaction costs even for the underlying.In your notation, P (the pricing model)=H (the hedging one)+continuous time delta hedga-transaction costs for the underlyingFor me in pricing model you assume perfect delta hedging so it will be a upper bound (statistically I mean) of the hedging model.

Last edited by frenchX on May 9th, 2011, 10:00 pm, edited 1 time in total.

QuoteOriginally posted by: TitanPartners Paul: Haha, is the only way forward to buy your book then ;-)Take heart from knowing that I make peanuts per copy! Some things are in papers that I can reference. But you won't get the 'golden thread' running through these ideas if you try to piece the papers together.P

I'm definitely interested.QuoteOriginally posted by: frenchX What I believe in is a combination of S(VM)² and UVM. Basically is a bit like fusionning SV and UVM. You will have a best case/worst case for the mean and the variance. You can imagine the worst value being mean_worst-eps*worst_variance and the best one being mean_best+eps*best_variance. Delta is choosen for each to cancel the directional risk and to minimize the variance. Then you built a static hedge to reduce your spread between best case/ worst case. Once you have that, you sell your exotic to your reduce best case (seller case) or you can buy it for your reduced worst case (buyer side). To agree with the market you can play a bit with eps (your risk aversion) to evaluate your loss.Once you have sell your exotic, you have to hedge it. Hedging can only be done discretely at one cost. The hedging model is very similar to the pricing one except that there is no continuous delta hedging. The underlying is seen as a call option with 0 strike and is incorporated in the semi static hedging. Being mark to market, this static hedging includes transaction costs even for the underlying.In your notation, P (the pricing model)=H (the hedging one)+continuous time delta hedga-transaction costs for the underlyingFor me in pricing model you assume perfect delta hedging so it will be a upper bound (statistically I mean) of the hedging model.Have you implemented an example of this?Oh, and interesting choice of words, 'I believe in'.....There's no point in replacing one faith based method with another, empiricism is what counts.

No running before walking!Here is the first reading assignment. Taken from PWOQF2. (Note that this is not PWIQF2, and it's not the first edition.)Let's start with Chapter 5, the Black-Scholes Model. Sections 5.1-5.7. This is to set the scene, giving an idea of the 'style' of maths to be used. This shouldn't be controversial. Classical derivation of the BS equation using stochastic calculus.Then move on to Chapter 12, How to Delta Hedge. This chapter introduces the idea of using stochastic calculus to exploit arbitrage opportunities. I think it's good to see how to make money before looking at calibration, which is designed to stop you making money! This is all quite straightforward. We won't be using much of this chapter but I think it helps put you in the right frame of mind! It does beg one question, and that is how do you forecast vol? I'd like to leave that subject until later on if I may.No asking questions until you've read those two chapters, as that would defeat the whole exercise.P

QuoteOriginally posted by: TinManI'm definitely interested.QuoteOriginally posted by: frenchX What I believe in is a combination of S(VM)² and UVM. Basically is a bit like fusionning SV and UVM. You will have a best case/worst case for the mean and the variance. You can imagine the worst value being mean_worst-eps*worst_variance and the best one being mean_best+eps*best_variance. Delta is choosen for each to cancel the directional risk and to minimize the variance. Then you built a static hedge to reduce your spread between best case/ worst case. Once you have that, you sell your exotic to your reduce best case (seller case) or you can buy it for your reduced worst case (buyer side). To agree with the market you can play a bit with eps (your risk aversion) to evaluate your loss.Once you have sell your exotic, you have to hedge it. Hedging can only be done discretely at one cost. The hedging model is very similar to the pricing one except that there is no continuous delta hedging. The underlying is seen as a call option with 0 strike and is incorporated in the semi static hedging. Being mark to market, this static hedging includes transaction costs even for the underlying.In your notation, P (the pricing model)=H (the hedging one)+continuous time delta hedga-transaction costs for the underlyingFor me in pricing model you assume perfect delta hedging so it will be a upper bound (statistically I mean) of the hedging model.Have you implemented an example of this?Oh, and interesting choice of words, 'I believe in'.....There's no point in replacing one faith based method with another, empiricism is what counts.Yes I will try to do that. I insist on the word "try" because first I'm far from being a computer genius in programming and second I don't have plenty of time (I'm writing my thesis at the moment) but it's worth to try. If you have an explicit soft for Heston model (or general stoch vol) with explicit euler (the classical one), the modification is easy. For the estimation of the parameters, the method described in the book of Paul is easy and efficient (with fokker planck).And for the believe word, it's more intuition than faith There are a lot of articles with very fancy pricing models which perform poorly in terms of hedging (a paper from Carol Alexander which show that the smile adjusted BS formula is better than Heston, or a paper about pricing with non normal distribution whose hedging is worse than classical BS).I could be wrong but not sure. The best would be to do an internship or a postdoc about that on that topic.

Last edited by frenchX on May 9th, 2011, 10:00 pm, edited 1 time in total.

QuoteOriginally posted by: PaulNo running before walking!Here is the first reading assignment. Taken from PWOQF2. (Note that this is not PWIQF2, and it's not the first edition.)Let's start with Chapter 5, the Black-Scholes Model. Sections 5.1-5.7. This is to set the scene, giving an idea of the 'style' of maths to be used. This shouldn't be controversial. Classical derivation of the BS equation using stochastic calculus.Then move on to Chapter 12, How to Delta Hedge. This chapter introduces the idea of using stochastic calculus to exploit arbitrage opportunities. I think it's good to see how to make money before looking at calibration, which is designed to stop you making money! This is all quite straightforward. We won't be using much of this chapter but I think it helps put you in the right frame of mind! It does beg one question, and that is how do you forecast vol? I'd like to leave that subject until later on if I may.No asking questions until you've read those two chapters, as that would defeat the whole exercise.POK, I read those and in the spirit of moving this along, what's next?

Let's wait until another two people have read them!P

OK, while we're waiting, some questions related to those chapters.I noticed you had a chart of a VIX day of the week seasonal. Do you think it is statistically significant,and, if so, do you have an economic explanation?When I used to work for a money manager, I found and we made use of a nice VIX quarterly seasonal, undoubtedly due to earnings season. But, it may have faded by now -- any thoughts on thecurrent existence of that one or other VIX seasonals?

I suspect that it's significant. I think I mentioned elsewhere that we occasionally postponed some trades to take advantage of it. However I don't recall doing any proper stats on it.P

Okay, I have read the relevant chapters as well.

OK, I've read the two chapters. What's next ?

Any questions on anything in those two chapters?P

No, no questions here.

Let look at Section 49.6 next. This will give you a quick overview of direction and possibilities.P

Last edited by Paul on May 18th, 2011, 10:00 pm, edited 1 time in total.

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