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Mic
Topic Author
Posts: 77
Joined: July 25th, 2001, 3:42 am

### What is smile option?

Hi,Could somebody tell me what smile option is and the difficulty of finding its value? Thanks.Mic

Paul
Posts: 11449
Joined: July 20th, 2001, 3:28 pm

### What is smile option?

Well, I know what the smile is, just the variation of implied vol with strike price. But a smile option? Dunno. I could imagine it being lots of different things.P

Mic
Topic Author
Posts: 77
Joined: July 25th, 2001, 3:42 am

### What is smile option?

Thanks, Paul.Oh, I wanted to know what smile is and I should have asked what the smile is.However, could you or somebody tell me the difficulty of the problem and the references for it? Thanks.Mic

Paul
Posts: 11449
Joined: July 20th, 2001, 3:28 pm

### What is smile option?

Sure, I'll tell you all about it...but you ought to make your forum profile public first!!! That goes for everyone out there...don't be shy! P

Mic
Topic Author
Posts: 77
Joined: July 25th, 2001, 3:42 am

### What is smile option?

Hi, I have made my profile public. People out there can know more about me. (Actually, they can only know where I come from)Mic

Paul
Posts: 11449
Joined: July 20th, 2001, 3:28 pm

### What is smile option?

Good! And welcome, person from Hong Kong!'Smile' refers to the variation of implied volatility with strike. In a world with perfectly constant vol (a common assumption in the old days) then, assuming option prices are correct, there'd be no smile.The big questions are how to interpret the smile, and how to use it.There are many reasons for the existence of the smile and I'm sure we'll talk about this a lot on these forums. One way of modeling this is to say that actual vol is a function of asset, S, and time, t. But then how do we find sigma(S, t)? This is what's known as an inverse problem; knowing the solution to a math problem (the option prices in the market), find out the coefficients in the equation (the volatility). Normally you'd expect to work the other way around, estimate vol and then find prices. Inverse problems can be badly behaved and this is certainly true of option pricing problems. A small change to a market price of an option can have a big effect on the actual vol, sigma(S, t).

Mic
Topic Author
Posts: 77
Joined: July 25th, 2001, 3:42 am

### What is smile option?

Thanks fot the explanation.So, does it imply that it is simply an inverse problem, an inverse problem thatthe option prices in the market are known and sigma(S, t) is to be got back?Got another question: Do the option prices in the market come from the real market? If they do, then the problem is semi-empirical--one has to draw the real option data from the real market.One more question:What is the significance/importance of the option with smile?Mic

Paul
Posts: 11449
Joined: July 20th, 2001, 3:28 pm

### What is smile option?

Yes, just an inverse problem, but one that is very sensitive to the initial data, the market prices. The market price does indeed come from the real market. It's common practice to quote option prices in terms of implied volatility, rather than a $amount. So you hear people talking about an option having a price of 22% vol. That just means take the Black-Scholes formula and plug in the known stock price, interest rate, strike...and a volatility of 0.22 and whatever answer you get is the real$ amount. So you can think of the inverse problem as inferring local sigma(S,t) from implied volatility!Why is this important? Because you have to know how to interpret and use the information 'contained in' the smile. Does the smile tell you what volatility is going to do in the future, for instance. It's common practice to calibrate your pricing model so that it matches market prices. But there are many ways of doing that depending on your vol model: deterministic vol, stochastic vol, uncertain vol, utility theory, 'equilibrium' pricing...Some make more sense than others, and some are easier to implement than others. Unfortunately, the easy-to-implement models don't make much sense and the good models are hard to implement! (Reminds me of "Your work is both original and true. Unfortunately, the parts that are true are not original, and the parts that are original are not true." Edgar Allan Poe???)

Mic
Topic Author
Posts: 77
Joined: July 25th, 2001, 3:42 am

### What is smile option?

I see and thanks.I suppose that option with smile is not a recent problem and has been raised for some time. So what approaches did people use to tackle the problem? What are the best/commonly accepted approaches up to now? And their weaknesses are?Mic

Paul
Posts: 11449
Joined: July 20th, 2001, 3:28 pm

### What is smile option?

There are three approaches1. Deterministic2. Stochastic3. Uncertainfor modelling almost anything financial.Then you've got to decide whether to calibrate/fit your model to1. Current market prices2. Historical data3. BothWhat's best and what's most practical are not necessarily the same! The criteria for judging models can be1. Speed of pricing/hedging2. Flexibility in new situations3. ProfitabilityI don't know of any model that's good in all categories. (And I don't know of many scientific tests of profitability of various models.)P

Mic
Topic Author
Posts: 77
Joined: July 25th, 2001, 3:42 am

### What is smile option?

Thank you for your explanations.It seems there is hardly an approach that can satisfy all parties!Mic

Aaron
Posts: 6433
Joined: July 23rd, 2001, 3:46 pm

### What is smile option?

My recollection is that it used to be very hard to get good price quotes for options far from the money. The bid/ask spreads were so large that it was hard to notice the smiles. Also, smiles mostly affect very low-priced out of the money options and in the money options that trade very close to intrinsic value. There wasn’t enough total money at risk in options to make price deviations on these marginal options significant. If you buy an option for $100, and the market goes against you so the option price should decline to$1, do you really care that it only goes down to $2? Or if the market goes in your favor so the option should be worth$200, does it matter that it sells for \$201?The main practical problem, even today with better markets and more money at risk, is in risk management. When you are trying to predict small probability events, the effect of volatility changes becomes very important. A volatility smile is just another way of saying that large underlying price movements are more likely than a Gaussian distribution predicts. So, for example, if you write out of the money puts on the stock market you have to know that if the market goes down sharply, your options will increase in price much faster than constant volatility computations indicate.

Mic
Topic Author
Posts: 77
Joined: July 25th, 2001, 3:42 am

### What is smile option?

Have found a book that talks about "smile" in pretty clear and simple terms: Neil A. Chriss's Black-Scholes and Beyond, option pricing models. Dr. Wilmott's book: option pricing, mathematical models and computation also has a brief mention of that.Mic

Paul
Posts: 11449
Joined: July 20th, 2001, 3:28 pm

### What is smile option?

Chriss's book is good for the classical approach to treating the vol smile, and standard market practice. I take a more sceptical view of the whole subject! (In the two-volume book, not OP.) The other book you must read is Nassim Taleb's 'Dynamic Hedging' for the practical trader approach. Bob Whaley has done some empirical work on the subject but I don't have the reference with me.P

Findus

### What is smile option?

Okay so we have options and swaps on variance and volatility. Anybody want to price up an option on a risk-reversal (or even a risk-reversal swap)?