Question
A financial institution just sold a European call option on 100,000 shares of a nondividend paying stock. The stock price is $49, the strike price
A financial institution just sold a European call option on 100,000 shares of a nondividend paying stock. The stock price is $49, the strike price is $50, the riskfree rate is 5% per annum, the stock price volatility is 20% per annum, the time to maturity is 20 weeks (or 20/52=0.3846 years). The financial institution decided to delta hedge the option using the BlackScholes model, with weekly rebalancing. The table below lists the price path of the stock:
Week | Stock price | Delta | Shares purchased | Cost of shares purchased ($000) | Total number of shares held | Cumulative cost including interest ($000) | Interest cost ($000) |
0 49
1 | 47.12 | ||||||
2 | 44.3 | ||||||
3 | 50.2 | ||||||
4 | 46.25 | ||||||
5 | 49.52 | ||||||
6 | 50.25 | ||||||
7 | 53.04 | ||||||
8 | 56.7 | ||||||
9 | 53.2 | ||||||
10 | 49.8 | ||||||
11 | 47.06 | ||||||
12 | 45.6 | ||||||
13 | 43.1 | ||||||
14 | 44 | ||||||
15 | 47.59 | ||||||
16 | 49.95 | ||||||
17 | 53.26 | ||||||
18 | 56.73 | ||||||
19 | 59.71 | ||||||
20 | 57.25 |
Complete the table in Excel
What is the cost of writing and hedging this option?
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