Hedging Asian options (Yang et al. (2011)). a) Compute the Asian option price f ( t ,
Question:
Hedging Asian options (Yang et al. (2011)).
a) Compute the Asian option price f(t,St,Λt) when Λt/T⩾K.
b) Compute the hedging portfolio allocation (ξt,ηt) when Λt/T⩾K.
c) At maturity we have f(T,ST,ΛT)=(ΛT/T−K)+, hence ξT=0 and ηTAT=ATe−rTA0(ΛTT−K)1{ΛT>KT}=(ΛTT−K)+.
d) Show that the Asian option with payoff (ΛT−K)+can be hedged by the self-financing portfolio
ξt=1St(f(t,St,Λt)−e−(T−t)r(ΛtT−K)h(t,1St(ΛtT−K)))
in the asset St and
ηt=e−rTA0(ΛtT−K)h(t,1St(ΛtT−K)),0⩽t⩽T in the riskless asset
Step by Step Answer:
a When Lambdat T geq K we have fleftt St LambdatightmathrmeTt rleftfracLambdatTKightSt frac1mathrmeT...View the full answer
Introduction To Stochastic Finance With Market Examples
ISBN: 9781032288277
2nd Edition
Authors: Nicolas Privault
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