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| − | In [[Principles of Corporate Finance|Principles of Corporate Finance]] a replicating portfolio is defined as the combination of:
| + | Replicating Portfolio |
| − | * Borrowing money
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| − | * Buying a ratio of stock
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| − | Such that you replicate exactly the payoff from one call option. The number of shares need to replicate one call is called the ''option delta'' or ''hedge ratio''.
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| − | Take the example of a stock with has a current stock price of \$80,- with a maximum downside potential of 25% drop and an upside of 33% increase. This means that the stock can move between
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| − | * \$60,-
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| − | * \$106,67,-
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| − | A call option for \$80,- in this case would be moving between:
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| − | * \$0,- (in the case there the stock price was below \$80,-)
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| − | * Between \$0,- and \$26,67 if the stock price was moving between and \$106,67,-
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| − | * \$26,67 (in the case the stock price was exactly \$106,67,-)
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| − | How should we value such a call option? There are two methods of calculation:
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| − | =Calculate option delta=
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| − | The option delta can be calculate as follows:
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| − | <math>\text{Option delta}</math> = <math>\frac{\text{Spread of option prices}}{\text{Spread of share prices}}</math>=<math>\frac{26.67 - 0}{106.67 - 60}</math>=<math>\frac{26.67}{46.67}</math>=<math>\frac{4}{7}</math>
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| − | <math>\frac{80 - ((4/7) \cdot 80)}{1.025}</math>= <math>33.45</math>
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| − | A more intuitive way of calculating the amount of money that needs to be borrowed is to simply subtract
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| − | The value of the call is then:
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| − | <math>\text{Value of call}</math> = <math>\text{Value of (4/7) shares}</math> - <math>\text{33.45 bank loan}</math> =
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| − | = <math>80 \cdot (4/7) - 33.45</math> = <math>12.26</math>
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| − | =Risk Neutral Valuation=
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| − | {{:Risk-Neutral Valuation}}
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| | [[Category:finance]] | | [[Category:finance]] |
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