By Antonio Mele, Yoshiki Obayashi
Fixed source of revenue volatility and fairness volatility evolve heterogeneously over the years, co-moving disproportionately in periods of world imbalances and every reacting to occasions of alternative nature. whereas the method for options-based "model-free" pricing of fairness volatility has been recognized for your time, little is understood approximately analogous methodologies for pricing a variety of fastened source of revenue volatilities.
This e-book fills this hole and gives a unified assessment framework of fastened source of revenue volatility whereas facing disparate markets equivalent to interest-rate swaps, executive bonds, time-deposits and credits. It develops model-free, ahead having a look indexes of fixed-income volatility that fit varied quoting conventions throughout a variety of markets, and uncovers sophisticated but very important pitfalls coming up from naïve superimpositions of the normal fairness volatility technique while pricing a number of fastened source of revenue volatilities.
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Additional info for The Price of Fixed Income Market Volatility
4 provides further results and intuition on the origins of these weightings. 3 Hedging While our derivations rely on the assumption that the forward risk is a continuoustime process, we can illustrate the main issues arising in our context while relying on a simple discrete-time example. 16) t=1 where N denotes the number of trading days over the year. 16) is the discrete-time counterpart to Eq. 12) and its first term can be expanded just as in Eq. 14). 17) t=1 where the second term can be replicated through a static position in out-of-themoney options and one at-the-money options as explained.
Indexes of expected volatility can then be formulated based on these variance contract designs. We shall return to the definition and properties of V bp (t, T ) in Sect. 5. 3 Interest Rate Variance Swaps The risks we study in this book are spanned by interest rate derivatives with payoffs such as those in Eq. 1). These payoffs have two components: (i) the forward risk, Xτ at τ = T , which we want to price the volatility of, and (ii) the market numéraire, NT , which links to the very nature of the derivative involved in the market of interest.
Replication is possible through replication of the forward risk Xt , rather than by trading the forward agreement through Eq. 18). Yet Xt may not be traded in situations of interest. For example, in Chap. 3, Xt is the forward swap rate, which cannot be perfectly hedged (it is not traded). However, we show that a model-free expression for the fair value of a variance swap is available under certain conditions, even when the risk Xt cannot be replicated. 2, which is less stringent than one requiring that a variance swap must be perfectly hedged.