Assume that your company has invested in 100,000 shares of Unglow plc, a manufacturer of light bulbs. You are concerned about the recent volatility in Unglow‟s share price due to the unpredictable weather in the United Kingdom. You wish to protect your company‟s investment from a possible fall in Unglow‟s share price until winter in three months‟ time, but do not wish to sell the shares at present. No dividends are due to be paid Uniglow during the next three months.
Uniglow‟s current share price: Sh.20 Call option exercise price: Sh.20 Time to expiry: 3 months
Interest rates (annual): 6%
Volatility of Uniglow‟s shares 50% (standard deviation per year)
Assume that option contracts are for the purchase or sale of units of 1,000 shares.
(i) Devise a delta hedge that is expected to protect the investment against changes in the share price until winter. Delta may be estimated using N(d1).
(ii) Comment upon whether or not such a hedge is likely to be totally successful.
(i)N(d1) is required in order to determine the delta hedge.
In order to protect against a fall in Uniglow‟s share price, the easiest hedge would be to write (sell) options on Uniglow‟s shares. A delta of 0.4222 means that the relevant hedge
(ii) A hedge such as this is only valid for a small change in the underlying share price. As the share price alters the option delta will alter and the hedge will need to be periodically re balanced.