Options on Credit Default Swaps and Credit Default Indexes

Credit variance risk premiums

“…In the following, we use the notation of Rutkowski (2012). Let $${T}_{0}\lt {T}_{1}\lt \text{\unicode{x022EF}}\lt {T}_{m}$$ denote the tenor structure of a forward‐start CDIS, where $${T}_{0}=T$$ is the inception date, $${T}_{m}$$ is the maturity date and $${T}_{j}$$ is the $$j$$th fee payment date for $$j=1,\text{\unicode{x02026}},m$$.…”

“…Consequently, randomness in $$P{V}_{T}(\kappa )$$ vanishes and $$P{V}_{T}({\kappa }_{U})$$ remains to be random with respect to $${\kappa }_{T}$$ only. We can rewrite the swaption payoff in Equation (1) to $$${(}^{{S}_{T}^{n}(\kappa )+{L}_{T}}={(}^{{S}_{T}^{a}(\kappa )},$$$ where $${S}_{T}^{a}(\kappa )={S}_{T}^{n}(\kappa )+{L}_{T}$$ denotes the loss‐adjusted forward CDIS and we have used the approximation $$P{V}_{T}(\kappa )n\approx P{V}_{T}({\kappa }_{T}){J}_{T}\approx {A}_{T}^{n}$$ (see Section 8.5.3 in Rutkowski, 2012). The price of the loss‐adjusted forward CDIS at time $$t\in [0,T]$$ is given by …”

“…Morini and Brigo (2011) refer to the default of all entities as the Armageddon event, whereas Rutkowski (2012) uses the term collapse event. The authors have shown that incorporating the event requires knowledge of the risk-neutral conditional distribution of τ n Rutkowski (2012). is silent on its estimation, whileMorini and Brigo (2011) resort to index tranches.…”

Credit Variance Risk Premiums

“…In the following, we use the notation of Rutkowski (2012). Let T 0 < T 1 < · · · < T m denote the tenor structure of a forward-start CDIS, where…”

“…t (κ) = E Q t (P n t ) − κE Q t (A n t ), 4Morini and Brigo (2011) refer to the default of all entities as the Armageddon event, whereas Rutkowski (2012) uses the term collapse event. The authors have shown that incorporating the event requires knowledge of the risk-neutral conditional distribution of τ n Rutkowski (2012). is silent on its estimation, whileMorini and Brigo (2011) resort to index tranches.…”