The Volatility Smile (Wiley Finance)

Emanuel Derman’s “The Volatility Smile” is an excellent book for those who have learned something about derivatives and now need to think on their own. More than just repeating known formulas and theorems, the author is always careful to distinguish between theories and models, alternating concepts and practice (including end-of-chapter exercises). I really enjoyed Chapters 14 to 18, dealing with Local Volatility and its consequences. As one of the first quants (Bruno Dupire being the other) to develop and publish a local volatility model, Derman explains clearly what is the goal of the model and shows how to observe and test its assumptions. Recommended for those who are learning quantitative finance and an useful addition even to experienced practitioners, who might benefit from the clear expositions in the book in order to better understand how far their results should carry and how better to communicate them.

Read the title for this review again. I purchased all the books he authored. They are all worth every penny, if he had charged more I would have paid it. I think he is giving us a discount to gain from his sleepless nights. All his books will be read and re-read. Thank you sir.

Emanuel Derman's books are always amazing and inspirational - My Life as A Quant, Models.Behaving.Badly and now The Volatility Smile, an excellent book full of insight and intuition, an outstanding guide for exciting volatility world!

As a textbook, it is really a wonderful introduction! Tell you many fundamental ideas. Love it.

I am only 6 chapters in but have been enjoying it.

When I worked at Nortel I occasionally got stock options. Suppose Nortel shares were trading at $100 per share. I would be given the option of buying, say, 50 shares in six months time at a strike price of $80 per share. Suppose Nortel stock went up in those six months to $120 per share. Those 50 shares would sell at $6,000. But I could buy them at $80, costing me $4,000. By buying at a discount and then immediately selling, I would realise a profit of $2,000. I guess they thought I would thereby be totally incentivized to work tirelessly for stock appreciation. As the Internet boom faded, I was seldom in the money. Nortel’s shares were under water, and my options were worthless. So at the time of issue, how should they have been priced? Plainly the closer the option expiry date to the option trade date, the less the share price uncertainty - which lowers the option price (often called the premium). However, if the shares are more volatile there is more chance that they will soar above the strike price - that’s got to raise the option price. The Black-Scholes equation is a partial differential equation which describes the rate of change of option price over time as a function of stock price. The stock price is assumed to be varying as a random walk around its trend with some volatility. The equation can be solved to give option prices, similar to the call option example I discussed above. Black-Scholes has just one unobservable parameter, the stock volatility. Other parameters in the model, the time to maturity, the strike price, the risk-free interest rate, and the current underlying stock price are all observable. In principle an option's theoretical value is a monotonically increasing function of implicit volatility. The Black-Scholes model implies that the stock price volatility is flat compared with the strike price. This is not empirically true. When running Black-Scholes in reverse, computing the implicit volatility from observed market rates for options (and using the other observable parameters), equities tend to have skewed curves: compared to at-the-money, implied volatility is substantially higher for low strikes, and slightly lower for high strikes. Commodities often have the reverse behaviour to equities, with higher implied volatility for higher strikes. This departure from linearity, when graphed, is termed the volatility smile. Naturally it is possible – at the expense of additional complexity – to factor in these non-linearities. And so we come to Derman’s and Miller’s book, “The Volatility Smile”. Aimed at practitioners who have already absorbed the standard Black-Scholes approach, this treatment looks in detail at several advanced models (local volatility, stochastic diffusion, jump-diffusion) which aim to provide a better match to real-life behaviour. Presenting itself as a mathematical textbook, albeit informed and motivated by market realities, the precondition for getting the best from this work is plainly a postgraduate qualification in mathematical finance. The book is really for working quants. Those with the right background will, however, find the presentation both relevant and lucid.

To explain the concepts, author relied on intuition first then on math.

Well written even for those with basic understanding of options math..

This is a great introductory book about volatility surface. It doesn’t assume much advanced knowledge about the subject but gradually helps you to build up your understanding through various examples and work in replicating portfolio. I would strongly recommend this for any quant who intends to step into this area.

Book cover came damaged.

Really good copy thanks

複製理論や二項モデルの導入後、Local volatility, Stochastic volatility, Jump modelの特徴、メリットやデメリットなどについてかみ砕いて紹介している。 前書きによればトレーディングデスク担当者が、モデルの挙動について洞察できるよう配慮して執筆したとのこと。 モデルの実装という点では他に名著があると思うが、クオンツ以外のオプション担当者にとってはスマイルモデルに関する知識はこの本で十分だと思う。 JIM GATHERAL氏のTHE VOLATILITY SURFACEと比べると数学的厳密性には拘らず、 近似的式変形を繰り返すことで式を簡略化し、モデルの本質的振る舞いを少しでも分かりやすく説明しようという親切心が伺える。 英文も平易で簡単な例題も散りばめられているので、少しブラックショールズや二項モデルの知識がある人ならば読み進められるだろう。

All you need to know about finance is here, the book explains the idea behind trading volatility, Emmanuel Derman excels at this topic and the books is comprehensible even if you don't have a masters in finance. Amazing book.