Engineering Convexity Positions
This chapter discusses the concept of convexity, benefits of volatility as well as convexity trading in the context of bonds and options. The notion of a delta-hedged bond portfolio is introduced. A partial differential equation consisting of the gains from convexity of long bonds and costs of maintaining the volatility position is discussed. We describe the intuition behind the Vasicek and Cox–Ingersoll–Ross models before presenting their associated pricing equations. We highlight similarities between a delta-hedged bond portfolio and option pricing and derive the Black–Scholes equation. Different sources of convexity such as mark-to-market, convexity by design, and prepayment options are discussed. ...
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