As the deal evolves our trading team starts getting pushed around the market and it dawns on us that the other bank s pricing is better than ours at least for this class of deals. We could fix this problem by inventing a universal method for achieving the best possible prices for all deal types. That topic will be covered in a future column next to the column on Elvis sightings. Here we focus on a single class of deals the constant maturity swaps caps and floors. We develop a framework that leads to the standard methodology for pricing these deals and then use this framework to systematically improve the pricing. Let us start by agreeing on basic notation.

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By using our site, you acknowledge that you have read and understand our Cookie Policy , Privacy Policy , and our Terms of Service. Quantitative Finance Stack Exchange is a question and answer site for finance professionals and academics. It only takes a minute to sign up. I am looking for help in understanding the algebraic derivation to go in between some of the lines in Pat Hagan's famous Convexity Conundrums paper e.

Just to be clear, 3. Then for 3. So this explains how 3. Next I'll look at 3. The expectation value of interest is. The second term is the usual expression for a call option, so in the Black scholes framework this is simply given by.

You can already spot these terms in expression 3. The other expectation value is a bit trickier, as we have. Then this expectation value becomes. This gives. Sign up to join this community.

The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Asked 4 years, 6 months ago. Active 4 years, 6 months ago. Viewed times. Randor Randor 1 1 gold badge 4 4 silver badges 18 18 bronze badges. However, you are asking people to read the paper and answer your question, which appears time consuming. It will be more helpful that you write out the steps and formulas and state where you do not understand. Active Oldest Votes. Cap Next I'll look at 3.

This should convince you that 3. Floor I'll leave you this one. Olaf Olaf 1, 12 12 silver badges 16 16 bronze badges. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. Featured on Meta.

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In the trenches. Convexity conundrums: Pricing CMS swaps, caps, and floors


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