Binary Options. Hamish Raw

      2.11 Answers

      1. Thetas are negative when out-of-the-money, positive when in the money and zero when at-the-money. Therefore,

      a) Positive

      b) Negative

      c) Zero

      d) Positive

      2. Since the $49 strike downbet and the $51 strike downbet are equidistant around the underlying they will have roughly the same absolute theta, i.e. 5.1. Therefore the $51 strike downbet will have a theta of roughly +5.1 since it is in the money and will therefore increase in value as time passes..

      3. Both a) and b) provide average thetas at the single points of 8 days and 7 days to expiry exactly. The former will underestimate the one day time decay while the latter will overestimate it; therefore c) will provide the most accurate forecast.

      4. Using the formula:

      Time Decay = 100 x (No. of Days x Theta ) / 365

      Bet 1: 100 ¥ ((1 ¥ 5) / 365) = 1.37 points

      Bet 2: 100 ¥ ((2 ¥ 5) / 365) = 2.74 points

      Bet 3: 100 ¥ ((5 ¥ 10) / 365) = 13.70 points

      5. Ignore t–2 and t+2, as the most accurate theta is obtained from making the increment in time as small as possible, i.e. as dt→0. Therefore subtracting the price at t+1 from the price at t–1 gives the difference in price over two days, and then multiplying by 365 and dividing by 100 provides the correct theta:

      Theta = [( Pt–1 – Pt+1 ) / ((t + 1) – (t – 1))]*365/100

      Bet 1 = [( 50.280 – 50.331 ) / (( t + 1 ) – ( t – 1))] ¥ 365 / 100 = –0.0931

      Bet 2 = [( 11.709 – 15.792 ) / (( t + 1 ) – ( t – 1))] ¥ 365 / 100 = –7.4515

      Bet 3 = [( 88.291 – 84.208 ) / (( t + 1 ) – ( t – 1))] ¥ 365 / 100 = 7.4515