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In derivative pricing, this is referred to as Gamma (Γ), one of the Greeks. In practice the most significant of these is bond convexity, the second derivative of bond price with respect to interest rates. As the second derivative is the first non-linear term, and thus often the most significant, "convexity" is also used loosely to refer to non ...
Convexity is a risk management figure, used similarly to the way 'gamma' is used in derivatives risks management; it is a number used to manage the market risk a bond portfolio is exposed to. If the combined convexity and duration of a trading book is high, so is the risk. [ 16 ]
As above, these methods can solve derivative pricing problems that have, in general, the same level of complexity as those problems solved by tree approaches, [1] but, given their relative complexity, are usually employed only when other approaches are inappropriate; an example here, being changing interest rates and / or time linked dividend policy.
Bond convexity is a measure of the sensitivity of the duration to changes in interest rates, the second derivative of the price of the bond with respect to interest rates (duration is the first derivative); it is then analogous to gamma. In general, the higher the convexity, the more sensitive the bond price is to the change in interest rates.
John Hull and Alan White, "The pricing of options on interest rate caps and floors using the Hull–White model" in Advanced Strategies in Financial Risk Management, Chapter 4, pp. 59–67. John Hull and Alan White, "One factor interest rate models and the valuation of interest rate derivative securities," Journal of Financial and Quantitative ...
Convexity is a geometric property with a variety of applications in economics. [1] Informally, an economic phenomenon is convex when "intermediates (or combinations) are better than extremes". For example, an economic agent with convex preferences prefers combinations of goods over having a lot of any one sort of good; this represents a kind of ...
Remember that an estimator for the price of a derivative is a random variable, and in the framework of a risk-management activity, uncertainty on the price of a portfolio of derivatives and/or on its risks can lead to suboptimal risk-management decisions. This state of affairs can be mitigated by variance reduction techniques.
In financial mathematics, the Ho-Lee model is a short-rate model widely used in the pricing of bond options, swaptions and other interest rate derivatives, and in modeling future interest rates. [1]: 381 It was developed in 1986 by Thomas Ho [2] and Sang Bin Lee. [3] Under this model, the short rate follows a normal process: