Advances in Risk Management

176 OPTIMAL INVESTMENT WITH INFLATION-LINKED PRODUCTS where the case ofγ=0 corresponds to the choice of the logarithmic utility ...

TARAS BELETSKI AND RALF KORN 177 Trautmann (1999)). To understand the qualitative behavior of the optimal strategy we look at th ...

178 OPTIMAL INVESTMENT WITH INFLATION-LINKED PRODUCTS we obtain: ψ 1 (t)= ∑ i:ti>t Ci I(t 0 ) exp(−rR(ti−t))+ Fexp(−rR(T−t)) ...

TARAS BELETSKI AND RALF KORN 179 0 5 10 15 t 20 25 30 220 200 180 160 140 120 100 80 60 I ( t) Figure 9.1Simulated path of an in ...

180 OPTIMAL INVESTMENT WITH INFLATION-LINKED PRODUCTS 0 0.45 0.5 0.55 0.6 0.65 0.7  ( 1 t) 0.75 0.8 0.85 0.9 0.95 51015 t 20 25 ...

TARAS BELETSKI AND RALF KORN 181 π 1 (t)∼ λσI−rR (1−γ)σ^2 I ( 1 + F ψ(t)I(t) ) , t→T, I(t)<I(t 0 ) This asymptotic behavior o ...

182 OPTIMAL INVESTMENT WITH INFLATION-LINKED PRODUCTS the inflation index if we would compare the actual amount of units of both ...

TARAS BELETSKI AND RALF KORN 183 only exception is if he is pretty sure that there will be a tendency for a huge increase of the ...

184 OPTIMAL INVESTMENT WITH INFLATION-LINKED PRODUCTS approach to portfolio optimization (see Korn (1997b)) is still valid but c ...

TARAS BELETSKI AND RALF KORN 185 which implies (with the notation of Korn (1997a)): ̃I(y)=(U′)−^1 (y)=cI(T)−½y leading to X(y)=E ...

186 OPTIMAL INVESTMENT WITH INFLATION-LINKED PRODUCTS (ii) The form of the hedging error obtained in Proposition 3 is quite natu ...

TARAS BELETSKI AND RALF KORN 187 with a corresponding minimal quadratic hedging error equalling, Var(B)E(I(T)^2 )+(E(B))^2 E((I( ...

188 OPTIMAL INVESTMENT WITH INFLATION-LINKED PRODUCTS 9.4.3 Numerical examples We are now illuminating the gains for our hedging ...

TARAS BELETSKI AND RALF KORN 189 Table 9.1Corresponding hedging errors Panel A σ 21 0.04 0 −0.04 xH 1 H 2 H 1 H 2 H 1 H 2 100 0 ...

190 OPTIMAL INVESTMENT WITH INFLATION-LINKED PRODUCTS Jarrow, R. and Yildirim, Y. (2003) “Pricing Treasury Inflation Protected S ...

CHAPTER 10 Model Risk and Financial Derivatives François-Serge Lhabitant 10.1 INTRODUCTION Since the introduction of option trad ...

192 MODEL RISK AND FINANCIAL DERIVATIVES stocks or bond traders, derivatives traders cannot sell an option contract, hedge it, p ...

FRANÇOIS-SERGE LHABITAN T 193 Table 10.1A few examples of model risk and its consequences Period Institution Problem Loss (M) 19 ...

194 MODEL RISK AND FINANCIAL DERIVATIVES in fact a patch against model errors – while section 10.4 discusses the role that finan ...

FRANÇOIS-SERGE LHABITAN T 195 with a view toward developing a theory that accounts for market imperfec- tions (for example, tran ...