a. Following is the European call & put option formula to calculate the value of call option under the Black-Scholes Model where K is the strike price
C = S*N (d1) - N (d2) *K*e ^ (-r*t)
P = Ke^–rt * N(–d2) – SN(-d1)
Where,
C = call value
P = Put value
S = current stock price
N = cumulative standard normal probability distribution
t = days until expiration
Standard deviation, SD = σ
K = option strike price
r = risk free interest rate
Formula to calculate d1 and d2 are -
d1 = {ln (S/K) +(r+ σ^2 /2)* t}/σ *√t
d2 = d1 – σ *√t
Or you can use excel in following manner to calculate the value of call option and put option:
INPUTS |
Outputs |
Value |
|
Standard deviation (Annual) σ |
15.00% |
d1 |
0.0601 |
Expiration (in Years) T |
0.08 |
d2 |
0.0168 |
Risk free rates (annual) r |
2.00% |
N(d1) |
0.5240 |
Current stock price (S) |
$50.00 |
N(d2) |
0.5067 |
Strike price (K) |
$50.00 |
B/S call Price |
0.9052 |
Dividend yield (annual) |
0 |
B/S Put Price |
0.8220 |
Call Price = $0.9052
Put Price = $0.8220
INPUTS |
Outputs |
Value |
|
Standard deviation (Annual) σ |
15.00% |
d1 |
-2.1410 |
Expiration (in Years) T |
0.08 |
d2 |
-2.1843 |
Risk free rates (annual) r |
2.00% |
N(d1) |
0.0161 |
Current stock price (S) |
$50.00 |
N(d2) |
0.0145 |
Strike price (K) |
$55.00 |
B/S call Price |
0.0123 |
Dividend yield (annual) |
0 |
B/S Put Price |
4.9207 |
Call Price = $0.0123
Put Price = $4.9207
INPUTS |
Outputs |
Value |
|
Standard deviation (Annual) σ |
15.00% |
d1 |
0.0851 |
Expiration (in Years) T |
0.17 |
d2 |
0.0238 |
Risk free rates (annual) r |
2.00% |
N(d1) |
0.5339 |
Current stock price (S) |
$50.00 |
N(d2) |
0.5095 |
Strike price (K) |
$50.00 |
B/S call Price |
1.3043 |
Dividend yield (annual) |
0 |
B/S Put Price |
1.1379 |
Call Price = $1.3043
Put Price = $1.1379
Formulas used in excel calculation:
1a. For a stock trading at $50 with 15% volatility and 2% risk free interest rate,...
1a. For a stock trading at $50 with 15% volatility and 2% risk free interest rate, find the prices of a one month put and call options with a strike price of $50. b. Determine the effect on both the put and call of increasing the strike price to $55 c. Determine the effect of doubling the time to maturity
show work, step by step and explain please. no excel. 1a. For a stock trading at $50 with 15% volatility and 2% risk free interest rate, find the prices of a one month put and call options with a strike price of $50. b. Determine the effect on both the put and call of increasing the strike price to $55 Determine the effect of doubling the time to maturity
Use an options calculator for the first 2 problems 1a prices of a one month put and call options with a strike price of $50 For a stock trading at $50 with 15% volatility and 2% risk free interest rate, find the Determine the effect on both the put and call of increasing the strike price to $55 b. Determine the effect of doubling the time to maturity C.
Problem1 A stock is currently trading at S $40, during next 6 months stock price will increase to $44 or decrease to $32-6-month risk-free rate is rf-2%. a. [4pts) What positions in stock and T-bills will you put to replicate the pay off of a European call option with K = $38 and maturing in 6 months. b. 1pt What is the value of this European call option? Problem 2 Suppose that stock price will increase 5% and decrease 5%...
You observe that the stock XYZ is currently trading at $8.50. The continuously compounded volatility is 20% p.a. The stock is due to pay a $0.25 dividend going ex-dividend in 1 month’s time. 3-month European call and put options written on XYZ trading at $0.65 and $0.45 respectively. The strike price on both options is $8.00. The continuously compounded risk free rate is 6%pa. a) Which theoretical Black-Scholes condition is violated? b) Clearly describe the arbitrage process you would perform...
On October 2, 2018, Tesla stock was trading $305.65. There are options on Tesla stock, Below are the yarigble inputs you require. Using the Black-Scholes-Merton model and Solyer, solve for the implied volatility that causes the option to be valued at $44.25. The appropriate risk free rate c.c. is 0.85%. These are European Options. Underlying So Call or Put Strike 306.65 Put 300.00 10/2/18 3/15/19 Today Maturity Time to Expiration Volatility Risk Free Rate 59.52% 0.85% #N/ A #N/A #N/A...
The current stock price of a non-dividend-paying stock is $50, the risk-free interest rate is 10% per annum, and the volatility is 30% per annum. a) According to the BSM model what is the price of a three-month European put option with a 2. strike of $50? What would be the price of this option if the stock is expected to pay a dividend of $1.50 in two months? b)
. Stock AXY is trading at AUD 53 and pays no dividends. If six-month maturity European call and put prices are equal when the strike price is AUD 60, what is the continuously compounded risk-free interest rate per annum?
1a) The current price of a stock is $43, and the continuously compounded risk-free rate is 7.5%. The stock pays a continuous dividend yield of 1%. A European call option with a exercise price of $35 and 9 months until expiration has a current value of $11.08. What is the value of a European put option written on the stock with the same exercise price and expiration date as the call? Answers: a. $5.17 b. $3.08 c. $1.49 d. $2.50...
A stock is worth £50 and the current 1-year risk free rate is 1%. A call option with a strike of £55 and 1-year to maturity has a premium of £2. A put option also exists with 1-year to maturity, the same strike price and a premium of £6.46 (to the nearest penny). Are there arbitrage opportunities available in this scenario? Explain how you have come to this judgement and the reasoning that underlies your logic. What are the potential...