- Financial Engineering 201
Suppose that the volatility increases toσ= 32% on day one. Let us compare
the results for delta-vega and delta hedging:
S(1/365) delta-vega delta
58. 00 − 5. 90 − 299. 83
58. 50 − 12. 81 − 261. 87
59. 00 − 16. 05 − 234. 69
59. 50 − 14. 99 − 218. 14
60. 00 − 9. 06 − 212. 08
60. 50 2. 27 − 216. 33
61. 00 19. 52 − 230. 68
61. 50 43. 17 − 254. 90
62. 00 73. 62 − 288. 74Exercise 9.7
Using the data in our ongoing example (stock price $60, volatility 30%,
interest rate 8%), construct a delta-rho neutral portfolio to hedge a short
position of 1,000 call options expiring after 90 days with strike price $60,
taking as an additional component a call option expiring after 120 days
with strike price $65. Analyse the sensitivity of the portfolio value to
stock price variations if the interest rate goes up to 9% after one day,
comparing with the previous results. What will happen if the interest
rate jumps to 15%?The examples above illustrate the variety of possible hedging strategies. The
choice between them depends on individual aims and preferences. We have not
touched upon questions related to transaction costs or long term hedging. Nor
have we discussed the optimality of the choice of an additional derivative instru-
ment. Portfolios based on three Greek parameters would require yet another
derivative security as a component. They could provide comprehensive cover,
though their performance might deteriorate if the variables remain unchanged.
In addition, they might prove expensive if transaction costs were included.
9.2 Hedging Business Risk ....................................
We begin by introducing an alternative measure of risk, related to an intuitive
understanding of risk as the size and likelihood of a possible loss.