Consider a European call option and a European put option on a non-dividend
paying stock S. You are given the following information:
(1) r = 0.04
(2) The current price of the call option VC (0) is by 0.15 greater than the current price of the put option
VP (0).
(3) Both the put and the call expire in 4 years.
(4) The put and the call have the same strikes equal to 70.
Find the spot price S(0) of the underying asset.
(a) 48.90
(b) 59.80
(c) 69.70
(d) 79.60
(e) None of the above

We can use **put-call parity** to solve this problem. The put-call parity relationship for European options on non-dividend-paying stocks is given by:

\[
V_C(0) - V_P(0) = S(0) - K e^{-rT}
\]

Where:
- \( V_C(0) \) is the price of the call option today.
- \( V_P(0) \) is the price of the put option today.
- \( S(0) \) is the spot price of the stock (what we are trying to find).
- \( K \) is the strike price (which is 70).
- \( r \) is the risk-free interest rate (which is 0.04).
- \( T \) is the time to maturity (which is 4 years).

We are given that:
\[
V_C(0) = V_P(0) + 0.15
\]

Substitute this into the put-call parity equation:

\[
(V_P(0) + 0.15) - V_P(0) = S(0) - 70 e^{-0.04 \times 4}
\]

Simplifying this:

\[
0.15 = S(0) - 70 e^{-0.16}
\]

Now, calculate \( e^{-0.16} \):

\[
e^{-0.16} \approx 0.8521
\]

Substitute this value into the equation:

\[
0.15 = S(0) - 70 \times 0.8521
\]
\[
0.15 = S(0) - 59.647
\]
\[
S(0) = 59.647 + 0.15 = 59.797
\]

Thus, the spot price \( S(0) \) is approximately **59.80**.

The correct answer is **(b) 59.80**.

---

Would you like further details or have any questions? Here are 5 related questions to expand your understanding:

1. How does put-call parity change if the stock pays dividends?
2. What is the significance of the time to maturity (T) in option pricing?
3. How does the risk-free rate (r) affect the prices of European options?
4. Can the put-call parity be used for American options? Why or why not?
5. How would increasing volatility affect the prices of both the call and put options?

**Tip:** The put-call parity formula is a powerful tool for understanding the relationship between call and put prices, especially for European options.

Consider a European call option and a European put option on a non-dividend paying stock S. You are given the following information: (1) r = 0.04 (2) The current price of the call option VC (0) is by 0.15 greater than the current price of the put option VP (0). (3) Both the put and the call expire in 4 years. (4) The put and the call have the same strikes equal to 70. Find the spot price S(0) of the underying asset. (a) 48.90 (b) 59.80 (c) 69.70 (d) 79.60 (e) None of the above

Learn how to find the spot price of a non-dividend-paying stock using the put-call parity formula for European options. This problem involves the given strike price of 70, a risk-free rate of 0.04, and a maturity of 4 years. Explore the detailed solution with step-by-step calculations, ideal for finance and economics students.

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