archived_user
New member
- Dec 7, 2011
- 0
- 0
I am quite confused with the following examples.
Example 1:
Demonstrate the arbitrage opportunity can be exploited. Assume we traded 100 call options with option options selling for $6.5 (Additional information, if we use binomial tree to calculate the call option price: the call option should be $5.14. Spot price of asset is $30 and chance of going up to $40 in next period is 55% while chance of going down to $22.5 is 45% )
The solution first calculates the hedge ratio (ie. delta which is equal to ($10-0)/($40-$22.5)=0.5714 shares per option. Thus, we need to purchase 57.14 shares.
and then it calculates the portfolio value in up-move. The value of portfolio = 57.14*40- (100*10)=1,286. i dunno understand why the value of short options is 100*10 instead of 100*0.5714*10.
Is that 1 option only covers 0.5714 shares?
I found another example in the book supporting what i think.
Example 2:
A owns 60,000 shares of Co. B Stock with spot price is $50. A call option with strike price of $50 is selling for $4 and has a delta of 0.6.
1. Calculate no. of option needed to create a delta hedge
2. Calculate the effect on portfolio value of $1 increase in the price of Co. B stock.
For part (1): no of option needed =60,000/0.6=100,000 options
For part (2): the total value of increase in the portfolio= 60,000*1 (total value increase of stock) - 0.6*100,000 (the total value decrease in short option)
In example 1, the short call option value = change in option value @ t=1 (i.e.$10) * no. of option (i.e.100) while in example 2, the value of short options = delta (i.e. 0.6) * number of options (i.e.100,000)*change in option value @t=1 (i.e.$1)
Example 1:
Demonstrate the arbitrage opportunity can be exploited. Assume we traded 100 call options with option options selling for $6.5 (Additional information, if we use binomial tree to calculate the call option price: the call option should be $5.14. Spot price of asset is $30 and chance of going up to $40 in next period is 55% while chance of going down to $22.5 is 45% )
The solution first calculates the hedge ratio (ie. delta which is equal to ($10-0)/($40-$22.5)=0.5714 shares per option. Thus, we need to purchase 57.14 shares.
and then it calculates the portfolio value in up-move. The value of portfolio = 57.14*40- (100*10)=1,286. i dunno understand why the value of short options is 100*10 instead of 100*0.5714*10.
Is that 1 option only covers 0.5714 shares?
I found another example in the book supporting what i think.
Example 2:
A owns 60,000 shares of Co. B Stock with spot price is $50. A call option with strike price of $50 is selling for $4 and has a delta of 0.6.
1. Calculate no. of option needed to create a delta hedge
2. Calculate the effect on portfolio value of $1 increase in the price of Co. B stock.
For part (1): no of option needed =60,000/0.6=100,000 options
For part (2): the total value of increase in the portfolio= 60,000*1 (total value increase of stock) - 0.6*100,000 (the total value decrease in short option)
In example 1, the short call option value = change in option value @ t=1 (i.e.$10) * no. of option (i.e.100) while in example 2, the value of short options = delta (i.e. 0.6) * number of options (i.e.100,000)*change in option value @t=1 (i.e.$1)