Have seen and read this topic yet?
https://www.elitetrader.com/et/thre...erton-bsm-is-wrong.349376/page-2#post-5189895
Choosing the Lognormal Mean for Black Scholes
- Thread starter LM3886
- Start date
https://www.elitetrader.com/et/thre...erton-bsm-is-wrong.349376/page-2#post-5189895
quoting "thecoder" aka "botpro" is pure lunacy. You are better off quoting the crazy homeless guy down the street on this topic.
But what does that thread have to do with LTCM's blow up?
The search landed there - I wasn't quoting anyone. Just pointed to destriero topic.
Once again ....... LTCM blew up using too much leverage with the BS model.
From Wikipedia which you will likely disregard:-
Black–Scholes in practice
The normality assumption of the Black–Scholes model does not capture extreme movements such as stock market crashes.
The assumptions of the Black–Scholes model are not all empirically valid. The model is widely employed as a useful approximation to reality, but proper application requires understanding its limitations – blindly following the model exposes the user to unexpected risk.[31][unreliable source?] Among the most significant limitations are:
Results using the Black–Scholes model differ from real world prices because of simplifying assumptions of the model. One significant limitation is that in reality security prices do not follow a strict stationary log-normal process, nor is the risk-free interest actually known (and is not constant over time). The variance has been observed to be non-constant leading to models such as GARCH to model volatility changes. Pricing discrepancies between empirical and the Black–Scholes model have long been observed in options that are far out-of-the-money, corresponding to extreme price changes; such events would be very rare if returns were lognormally distributed, but are observed much more often in practice.
Nevertheless, Black–Scholes pricing is widely used in practice,[2]:751[32] because it is:
Useful approximation: although volatility is not constant, results from the model are often helpful in setting up hedges in the correct proportions to minimize risk. Even when the results are not completely accurate, they serve as a first approximation to which adjustments can be made.
Basis for more refined models: The Black–Scholes model is robust in that it can be adjusted to deal with some of its failures. Rather than considering some parameters (such as volatility or interest rates) as constant, one considers them as variables, and thus added sources of risk. This is reflected in the Greeks (the change in option value for a change in these parameters, or equivalently the partial derivatives with respect to these variables), and hedging these Greeks mitigates the risk caused by the non-constant nature of these parameters. Other defects cannot be mitigated by modifying the model, however, notably tail risk and liquidity risk, and these are instead managed outside the model, chiefly by minimizing these risks and by stress testing.
Explicit modeling: this feature means that, rather than assuming a volatility a priori and computing prices from it, one can use the model to solve for volatility, which gives the implied volatility of an option at given prices, durations and exercise prices. Solving for volatility over a given set of durations and strike prices, one can construct an implied volatility surface. In this application of the Black–Scholes model, a coordinate transformation from the price domain to the volatility domain is obtained. Rather than quoting option prices in terms of dollars per unit (which are hard to compare across strikes, durations and coupon frequencies), option prices can thus be quoted in terms of implied volatility, which leads to trading of volatility in option markets.
Black–Scholes in practice
The normality assumption of the Black–Scholes model does not capture extreme movements such as stock market crashes.
The assumptions of the Black–Scholes model are not all empirically valid. The model is widely employed as a useful approximation to reality, but proper application requires understanding its limitations – blindly following the model exposes the user to unexpected risk.[31][unreliable source?] Among the most significant limitations are:
- the underestimation of extreme moves, yielding tail risk, which can be hedged with out-of-the-money options;
- the assumption of instant, cost-less trading, yielding liquidity risk, which is difficult to hedge;
- the assumption of a stationary process, yielding volatility risk, which can be hedged with volatility hedging;
- the assumption of continuous time and continuous trading, yielding gap risk, which can be hedged with Gamma hedging.
Results using the Black–Scholes model differ from real world prices because of simplifying assumptions of the model. One significant limitation is that in reality security prices do not follow a strict stationary log-normal process, nor is the risk-free interest actually known (and is not constant over time). The variance has been observed to be non-constant leading to models such as GARCH to model volatility changes. Pricing discrepancies between empirical and the Black–Scholes model have long been observed in options that are far out-of-the-money, corresponding to extreme price changes; such events would be very rare if returns were lognormally distributed, but are observed much more often in practice.
Nevertheless, Black–Scholes pricing is widely used in practice,[2]:751[32] because it is:
- easy to calculate
- a useful approximation, particularly when analyzing the direction in which prices move when crossing critical points
- a robust basis for more refined models
- reversible, as the model's original output, price, can be used as an input and one of the other variables solved for; the implied volatility calculated in this way is often used to quote option prices (that is, as a quoting convention).
Useful approximation: although volatility is not constant, results from the model are often helpful in setting up hedges in the correct proportions to minimize risk. Even when the results are not completely accurate, they serve as a first approximation to which adjustments can be made.
Basis for more refined models: The Black–Scholes model is robust in that it can be adjusted to deal with some of its failures. Rather than considering some parameters (such as volatility or interest rates) as constant, one considers them as variables, and thus added sources of risk. This is reflected in the Greeks (the change in option value for a change in these parameters, or equivalently the partial derivatives with respect to these variables), and hedging these Greeks mitigates the risk caused by the non-constant nature of these parameters. Other defects cannot be mitigated by modifying the model, however, notably tail risk and liquidity risk, and these are instead managed outside the model, chiefly by minimizing these risks and by stress testing.
Explicit modeling: this feature means that, rather than assuming a volatility a priori and computing prices from it, one can use the model to solve for volatility, which gives the implied volatility of an option at given prices, durations and exercise prices. Solving for volatility over a given set of durations and strike prices, one can construct an implied volatility surface. In this application of the Black–Scholes model, a coordinate transformation from the price domain to the volatility domain is obtained. Rather than quoting option prices in terms of dollars per unit (which are hard to compare across strikes, durations and coupon frequencies), option prices can thus be quoted in terms of implied volatility, which leads to trading of volatility in option markets.
Thank you for bring that thread up. If I saw it earlier many of my questions would have been answered. I think @destriero attributed the long-term average stock growth to volatility instead of mean. I was confused because it is different from statistics text, where sample variance is computed after removing sample mean.
I don't think you will succeed speaking much wisdom into this guy. If you look at his post history he is not all that interested in facts but rather looks for some backup on the internet that supports his claims. Some of the cited material does not even support his claim, for example the above wiki article actually supports your earlier statements and common knowledge. Hard to argue with someone who can't be wrong even when facts contradict his opinion.
How does one use BS in bond basis statistical arbitrage?
One does not because it's an equity based model. Fixed income uses completely different models because basic bs does not capture (purposely) any interest rate dynamics with brownian motion (stochasticity) . But in his eyes you must be wrong by default.
Even simple rates based or futures based options use the black model that rather focuses on the diffusion of the forward price rather than spot price
Even simple rates based or futures based options use the black model that rather focuses on the diffusion of the forward price rather than spot price
while the wiki shares some of the shortcomings of the models it clearly explains why it’s still used by banks and other firms. Why would you post something that proves black scholes is a decent framework?