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Mid curve swaption

Last modified by Nikita Kapchenko on 2019/08/26 18:08

A mid-curve swaption is a European style option on an underlying forward starting swap.

The only difference with standard vanilla swaption is that there is a start time delay between option expiry and the real start of underlying swap.

Payoff description:

  • t - pricing date
  • Texp - option expiry
  • Tstart - underlying swap start date
  • Tend - underlying swap end date

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[+] Notations

Pricing

Full mid curve pricing chain (with copula model)

mco_chart.png

Mid curve payoff as a function of swap rates only:

After Mid curve option replication the premium becomes the function of two simple swap rates and their annuities.

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[+] Expectations computed under different measures

After TSR replication, the premium becomes the function of two simple swap rates only! 

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Copula

My choice for pricing mid curve is gaussian copula model.