How do you calculate the arbitrage strategy and the PV of the dividend? Having a rough time with this concept.
Table 2
| European call option on Lotus equity | $3 |
| European put option on Lotus equity | $4 |
| Lotus equity price | $50 |
| Time to expiration of options | 4 months |
| Exercise price of options | $50 |
| Risk-free rate | 10% |
| Dividend to be paid in 3 months | $2 |
Arbitrage is a financial strategy used to profit from price disparities between related securities or assets. In this scenario, we have European call and put options on Lotus equity, with a given equity price, time to expiration, exercise price, risk-free rate, and a dividend to be paid. Let’s break down the steps to calculate an arbitrage strategy and the present value (PV) of the dividend.
Ulue
FV is the future value (the dividend) which is $2
r is the interest rate (the risk-free rate) which is 10% or 0.10
n is the number of periods (time in years), which is 3/12 (3 months converted to years)
Plug these valunderstand the Situation: We have European call and put options with the following details:
Call Option Price: $3
Put Option Price: $4
Lotus Equity Price: $50
Time to Expiration: 4 months
Exercise Price: $50
Risk-Free Rate: 10%
Dividend to be Paid in 3 Months: $2
Arbitrage Strategy: Arbitrage seeks to exploit price differences between related assets. In this case, we can use a combination of options to create a risk-free profit.
a. Cash-and-Carry Arbitrage: One common arbitrage strategy involves the “cash-and-carry” principle. This strategy aims to take advantage of differences between the cost of financing and the expected returns. Here’s how you can use it:
Step 1: Buy the European call option for $3.
Step 2: Short sell the European put option for $4.
Step 3: Invest the proceeds from the short sale in a risk-free asset (e.g., a bond) to earn the risk-free rate.
The goal of this strategy is to ensure that the initial investment cost is less than the present value of the expected cash flows from the options. If the cost is less, it presents an arbitrage opportunity. You will need to calculate the exact values based on the given parameters and ensure that the arbitrage condition is met.
Present Value (PV) of Dividend: To calculate the present value of the $2 dividend to be paid in 3 months, we can use the formula for present value:
PV = FV / (1 + r)^n
es into the formula:
PV = $2 / (1 + 0.10)^(3/12)
PV ≈ $1.975
The present value of the $2 dividend to be paid in 3 months is approximately $1.975.
In conclusion, arbitrage strategies aim to take advantage of price differences in financial instruments to make risk-free profits. In this case, you can consider a cash-and-carry arbitrage strategy using the provided call and put option prices. Additionally, to calculate the present value of the $2 dividend, you can use the present value formula with the risk-free rate. Please note that actual arbitrage calculations may involve more complex factors and should be performed carefully based on real-time market conditions.
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