Exercise Solution 8.12

  1. Our timeline has form
  2. To specify a primary mapping, we need five key factors. To determine if the option knocks in, we need the London afternoon fixing price of gold for each of the option’s four remaining trading days until expiration. The last of these will also be used to determine the option’s expiration value. We use the spot-next Libor rate for actual day 4 (the date the option expires) to accumulate the option’s expiration value from actual day 8 (the option’s settlement date) to actual day 9 (the value date for the last day of the VaR horizon). Accordingly, we define


  3. To specify a primary portfolio mapping, we first specify assets and define the portfolio’s value in terms of these. For this exercise, there will be a single asset, so this is largely a formality.We specify the single asset 1S1 to represent the price of an up-and-in barrier call option on one ounce of gold. Holdings are ω = 10,000. We define the mapping


    Next, we define mapping map 1S1 = φ(1R) in the manner described in part (b) above:


    Composing ω with φ, we obtain our primary mapping: