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The following text of Kaplan is available at: https://kfknowledgebank.kaplan.co.uk/KFKB/Wiki%20Pages/Black%20Scholes%20option%20pricing%20model.aspx?mode=none
This text states:
“An investor can eliminate the risk of his shareholding by constructing a “delta hedge”.
An investor who holds a number of shares and sells (an option writer) a number of call options in the proportion dictated by the delta/the hedge ratio ensures a hedged portfolio. N.B. A hedged portfolio is one where the gains and losses cancel out against each other.
Number of option calls to sell = Number of shares held/N(d1).”The questions are as follows:
1) Investor acts as an option writer? Like a bank? Is it an unusual viewpoint for P4, isn’t it?
Please clarify what is meant by selling call options.2) Could I simply consider that: “to sell call options” is literally the same a “to buy put options”?
3) If I consider the the hedge as a purchase of a put option, therefore I should assess Delta as N(-d1) (which is opposed to N(d1) for a call option above).
4) However, if so, the Delta will be different as N(d1) is not the same as N(-d1). Therefore, the hedge of the same nature won’t be the same which is obviously incorrect. So, please help me to understand the essence.
Thank you in advance.
I don’t think you can have watched the free lecture on options, which will help you with this questions.
1 What the text says is correct. However, in practice it is usually the option dealer who will buy shares in order to hedge against the risk on the options they are selling. It doesn’t affect the arithmetic at all, but it is them who will be wanting to create the delta hedge.
2 No – selling call options is not the same as buying put options. They will both protect against the risk to a degree (so in that sense the same affect) but they will have different prices (depending on which was the share price is expected to move).
3 You should not consider the purchase of a put option (unless the question tells you to). If you are asked to value a put option then you should use the put-call parity formula on the formula sheet (unless the question tells you to use N(-d1)
4 see the answer to 3 🙂
1) So, usually it’s like as follows which is mentioned in the text as well:
“Alternatively, if you have already written call options, then a delta hedge can be constructed by buying shares. Number of shares to hold = Number of call options sold × N(d1).”
It’s clear.2) Purchase of put option implies the premium paid being the major cost, whereas selling of call option naturally stipulates costs that are determined by the fact whether the sold option is excercised or not. It’s still determined by stirke price and actual price, though the option seller bears much higher risks compared to counterparty. It’s the seller who bears the extreme risks upside risks (if any). Am I correct?
3) However, P4 syllabus and questions are mainly related to those who purchase the options. Frankly, I’ve never seen a question where an entity sells options. So, I should not spend too much time for meditations on issues related to selling an option. Am I correct?
Thank you in advance.
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