Question

**A stock is currently traded for $135. The risk-free rate
is 0.5% per year (continuously compounded APR) and the stock’s
returns have an annual standard deviation (volatility) of 56%.
Using the Black-Scholes model, we can find prices for a call and a
put, both expiring 60 days from today and having strike prices
equal to $140.**

**(a) What values should you use for S, K, T−t, r, and σ
in the Black-Scholes formula?**

**S =**

**K =**

**T - t =**

**r =**

**σ =**

**(b) Find the d1 and d2 to be used in the Black-Scholes
formula.**

**d1 =**

**d2 =**

**(c) Using these d1 and d2, find the call price Ct and
put price Pt according to the Black-Scholes formula.**

**Ct =**

**Pt =**

Answer #1

Proper solution is given.

Assume risk-free rate is 5% per annum continuously compounded.
Use Black-Scholes formula to find the price the following
options:
European call with strike price of $72 and one year to maturity
on a non-dividend-paying stock trading at $65 with volatility of
40%.
European put with strike price of $65 and one year to maturity
on a non-dividend-paying stock trading at $72 with volatility of
40%

Find the current fair values of a D1 month European call and a
D2 month European put option, using a current stock price of D3,
strike price of D4, volatility of D5, interest rate of D6 percent
per year, continuously, compounded. Obtain the current fair values
of the following:
1.European call by simulation.
2.European put by simulation.
3.European call by Black-Scholes model.
4.European put by Black-Scholes model.
D1
D2
D3
D4
D5 D6
11.2
10.9
31.7
32.6
0.65 9.5

A call option has 20 days to mature. The continuously compounded
annual risk free rate is 1%. The stock price is 28.40. The exercise
price is 29. The annualized volatility is 0.27. Dividend yield is
zero. What is the delta of this option? What is the Black-Scholes
put price for the data of above question?

A stock’s current price S is $100. Its return has a volatility
of s = 25 percent per year. European call and put options trading
on the stock have a strike price of K = $105 and mature after T =
0.5 years. The continuously compounded risk-free interest rate r is
5 percent per year. The Black-Scholes-Merton model gives the price
of the European put as:
please provide explanation

In addition to the five factors, dividends also affect the price
of an option. The Black–Scholes Option Pricing Model with dividends
is:
C=S×e−dt×N(d1)−E×e−Rt×N(d2)C=S×e−dt×N(d1)−E×e−Rt×N(d2)
d1=[ln(S/E)+(R−d+σ2/2)×t](σ−t√)d1= [ln(S /E ) +(R−d+σ2/2)×t ] (σ−t)
d2=d1−σ×t√d2=d1−σ×t
All of the variables are the same as the Black–Scholes model
without dividends except for the variable d, which is the
continuously compounded dividend yield on the stock.
A stock is currently priced at $88 per share, the standard
deviation of its return is 44 percent...

A stock is currently trading at $25.85. It is not expected to
pay dividends over the next year. You price a six-month call option
on the stock with a strike of K=15 using the Black-Scholes model
and find the following numbers: d1=2.115 d2=1.832 N(d1)=0.983
N(d2)=0.967 Given this information, the delta of the call is
Multiple Choice
0.983
0.967
2.115
1.832

A stock index currently stands at 300 and has a volatility of
20%. The risk-free interest rate is 8% and the dividend yield on
the index is 3%.
Use the Black-Scholes-Merton formula to calculate the price of
a European call option with strike price 325 and the price of a
European put option with strike price of 275. The options will
expire in six months.
What is the cost of the range forward created using options in
Part (a)?
Use...

A stock index level is currently 2,000. Its volatility is 25%.
The risk-free rate is 4% per annum (continuously compounded) for
all maturities and the dividend yield on the index is 2%. Using the
Black-Scholes model:
a) Derive the value a 6-month European put option with a strike
price of 2020.
b) Derive the position in the index that is needed today to
hedge a long position in the put option. Assume that the option is
written on 250 times...

A stock index is currently 1,500. ITs volatility is 18% per
annum. The continuously compounded risk-free rate is 4% per annum
for all maturities.
(1) Calculate values for u,d, and p when a six-month time step
is used.
(2) Calculate the value a 12-month American put option with a
strike price of 1,480 given by a two-step binomial tree.

Use Excel and anwer the question.
The year-end values for the past 10 years of KOSPI200 are as
follows(2010~2019).
271.19 238.08 263.92 264.24 244.05 240.38 260.01 324.74 261.98
293.77
Compute the volatility per annum. The risk free rate is 3
percent per annum and the current value of KOSPI200 is 290. Use the
Black-Scholes OPM and calculate the prices of European call and put
options with a strike price of 285 and the time to maturity of 6
months. You...

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