question archive In this task there is 8 European options on OMX index
In this task there is 8 European options on OMX index
Subject:EconomicsPrice: Bought3
In this task there is 8 European options on OMX index. Assume that all options have a term of 2 months ( ???? = 2/12). The risk-free interest rate, r (annual interest rate), on an annual basis was 5.5% for the term at this time. The discount factor with this interest rate is calculated, as we are perhaps most used to seeing it, ???? (????) = 1/ (1 + ????) ^????
Alternatively, the discount factor can be calculated as it appears in the Black-Scholes formula where the interest rate is noted with a continuous return on an annual basis, ???? (????) = ???? − ????continuous^????. The continuous interest rate is calculated according to ????continuous = ???????? (1 + ????annual interest rate) = 5.354%. Note that the two ways of calculating the discount factor are completely equivalent and that ???????? (????) = ???? (????) ???? constitutes the present value of the option's exercise price K.
End date = 2002-01-25 NOTE: Assume a remaining term of 2 months. Unit SEK.
OMX 2001-11-21 Redemption price Call options Sell options
S (at t = 0) K C P
829 780 79.75 23.25
829 800 67.00 29.25
829 900 17.25 78.38
829 1000 2.50 157.50
Historical volatility on an annualized basis for the OMX index: ???? = 0.3475
a. To be able to use the Black-Scholes formula to price options, you need to have a measure of the volatility of the underlying asset. One way to estimate volatility is to calculate the standard deviation of historical data for the underlying asset. Use the historical volatility ???? = 0.3475 and calculate the price of the four call options using the Black-Scholes formula. Comment on the results and compare with how the market priced the call options in above. Why do you think that the results are different? Discuss above all based on the model's assumptions and to what extent they correspond to reality.
