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Black-Scholes in the real world
- Thread starter OptionStudent
- Start date
To reply to the inital question: use the Black Model as suggested (wikipedia is good on this). This means in generalised Black Scholes model formula set S=F (the future price). Set b=0. Sigma you can play around with to match market prices either manually or as suggested using some iterative process to guess closer and closer.
Quickstrike (free on CME website) is good for playing around with checking your own calculations as it gives sigma (aka implied volatility) for end of day settlements etc.
Also, please no-one think of Black-Scholes as anything other than a formula for translating between market prices and implied vols (and for getting greeks). When people who don't know starting calling it a model things get confused.
Quickstrike (free on CME website) is good for playing around with checking your own calculations as it gives sigma (aka implied volatility) for end of day settlements etc.
Also, please no-one think of Black-Scholes as anything other than a formula for translating between market prices and implied vols (and for getting greeks). When people who don't know starting calling it a model things get confused.
Quiet1's post encourages me to rejoin this thread, which I started with what was intended to be a simple, practical question. In discussing the difference between a "formula" and a "model," Quiet1 is operating on turf where I am more comfortable than I am when reading trading tables. Black-Scholes is clearly both a formula and a model. There is an underlying model, albeit an unrealistic one that contains a parameter (forward-looking volatility) that is impossible to measure. Crowd-sourcing of volatility estimates to the market, under the rubric "implied volatility," introduces a circular element into Black-Scholes pricing. This is a problem, but a large academic literature shows that it is not an altogether fatal one. More serious is the unrealism of the assumptions underlying Black-Scholes-Merton. However, recall that Milton Friedman famously said that “Truly important and significant hypotheses will be found to have assumptions that are wildly inaccurate descriptive representations of reality and, in general, the more significant the theory, the more unrealistic the assumptions.” His point was that anyone can generate realistic models, but all they do is summarize data. Truly significant models give some insights into why markets and the economy behave as they do. Black-Scholes-Merton clearly qualifies by this criterion. It showed that rational pricing of futures contracts based on intangible assets such as stock indices does not depend on long-term trends in the stock index, only on its fluctuations about those trends, and it defined an arbitrage strategy that greatly reduces the gambling element in writing the contracts. The model did all that despite its unrealistic assumptions and circularity. Not bad.
I have learned a lot from this thread--thanks again to those who posted on it. I am still left guessing at the answer to my original question, which I now realize was poorly framed. Here is a rephrasing:
1. Current S&P 500 is 2610.
2. I want to buy an At the Money put expiring at the end of June.
3. I go to http://www.cmegroup.com/trading/equ...ration=M8&optionProductId=136&strikeRange=ATM
and learn that there is active trading in puts with a strike price listed at 261000.0 (evidently reflecting the odd convention of listing strike prices in pennies). These puts are currently settling for 58.50.
Now my question: Suppose I buy one at this price and hold it until expiration. Further suppose the S&P 500 tanks to 2500 between now and the end of June. Ignoring transaction costs, how much will the market maker who originally wrote the contract owe me?
I think the answer is $110 for a profit of $110 - $58.50 = $51.50. However, I only got there by applying common sense and tips from this thread. I found the fine print at the CME Group web site unhelpful, even misleading. On the other hand, I may still be out to lunch.
I have learned a lot from this thread--thanks again to those who posted on it. I am still left guessing at the answer to my original question, which I now realize was poorly framed. Here is a rephrasing:
1. Current S&P 500 is 2610.
2. I want to buy an At the Money put expiring at the end of June.
3. I go to http://www.cmegroup.com/trading/equ...ration=M8&optionProductId=136&strikeRange=ATM
and learn that there is active trading in puts with a strike price listed at 261000.0 (evidently reflecting the odd convention of listing strike prices in pennies). These puts are currently settling for 58.50.
Now my question: Suppose I buy one at this price and hold it until expiration. Further suppose the S&P 500 tanks to 2500 between now and the end of June. Ignoring transaction costs, how much will the market maker who originally wrote the contract owe me?
I think the answer is $110 for a profit of $110 - $58.50 = $51.50. However, I only got there by applying common sense and tips from this thread. I found the fine print at the CME Group web site unhelpful, even misleading. On the other hand, I may still be out to lunch.
this is very simplified but......he doesn't owe you anything. when you purchased the put you became the owner of the contract which will fluctuate in regard to all the various aspects of option pricing (greeks).Quiet1's post encourages me to rejoin this thread, which I started with what was intended to be a simple, practical question. In discussing the difference between a "formula" and a "model," Quiet1 is operating on turf where I am more comfortable than I am when reading trading tables. Black-Scholes is clearly both a formula and a model. There is an underlying model, albeit an unrealistic one that contains a parameter (forward-looking volatility) that is impossible to measure. Crowd-sourcing of volatility estimates to the market, under the rubric "implied volatility," introduces a circular element into Black-Scholes pricing. This is a problem, but a large academic literature shows that it is not an altogether fatal one. More serious is the unrealism of the assumptions underlying Black-Scholes-Merton. However, recall that Milton Friedman famously said that “Truly important and significant hypotheses will be found to have assumptions that are wildly inaccurate descriptive representations of reality and, in general, the more significant the theory, the more unrealistic the assumptions.” His point was that anyone can generate realistic models, but all they do is summarize data. Truly significant models give some insights into why markets and the economy behave as they do. Black-Scholes-Merton clearly qualifies by this criterion. It showed that rational pricing of futures contracts based on intangible assets such as stock indices does not depend on long-term trends in the stock index, only on its fluctuations about those trends, and it defined an arbitrage strategy that greatly reduces the gambling element in writing the contracts. The model did all that despite its unrealistic assumptions and circularity. Not bad.
I have learned a lot from this thread--thanks again to those who posted on it. I am still left guessing at the answer to my original question, which I now realize was poorly framed. Here is a rephrasing:
1. Current S&P 500 is 2610.
2. I want to buy an At the Money put expiring at the end of June.
3. I go to http://www.cmegroup.com/trading/equ...ration=M8&optionProductId=136&strikeRange=ATM
and learn that there is active trading in puts with a strike price listed at 261000.0 (evidently reflecting the odd convention of listing strike prices in pennies). These puts are currently settling for 58.50.
Now my question: Suppose I buy one at this price and hold it until expiration. Further suppose the S&P 500 tanks to 2500 between now and the end of June. Ignoring transaction costs, how much will the market maker who originally wrote the contract owe me?
I think the answer is $110 for a profit of $110 - $58.50 = $51.50. However, I only got there by applying common sense and tips from this thread. I found the fine print at the CME Group web site unhelpful, even misleading. On the other hand, I may still be out to lunch.
if at the contracts expiry the index is at 2500 your 2610 put would be worth about 110 which you could sell to monetize your position.
this is very simplified but......he doesn't owe you anything. when you purchased the put you became the owner of the contract which will fluctuate in regard to all the various aspects of option pricing (greeks).
if at the contracts expiry the index is at 2500 your 2610 put would be worth about 110 which you could sell to monetize your position.
Thanks sss12, I think I get the point. The party who initially wrote the contract was out of the picture as soon as he or she sold it. The contract's value will fluctuate as time to expiration decreases and the stock index changes. If I want to monetize, I would have to sell the contract before it expires but should be able to do so for a price that would converge on ~$110, in my example, as expiration approached. I am sure there are messy issues concerning the actual timing of when trading stops for contracts with a particular expiration date, and I also realize that most contracts are not held to expiration but are closed out by offsettig trades at some earlier date. However, dealing with the ins and outs of these practicalities is above my pay grade. I am just a student. Actually trading these cotracts would scare the hell out of me.