Question
In: Finance
A stock price is currently $50. It is known that at the end of one year...
A stock price is currently $50. It is known that at the end of one year it will be either $40 and $60. The exercise price of a one-year European call option is $55. The risk free interest rate is 5% per annum.
a. construct a binomial tree to show the payoff of the call option at the expiration date.
b. based on the binomial tree model, what is the value of the call option?
c. Address the relation between the binomial tree model and the Black-Scholes model
Solutions
Expert Solution
c) Relationship between binomial and black scholes model is that binomial model converges to black scholes model when the number of steps of binomial increases. In essence, black scholes model has infinite number of binomial steps.
jeff jeffy answered 2 years agoRelated Solutions
A stock price is currently $50. It is known that at the end of one year...
A stock price is currently $50. It is known that at the end of
one year it will be either $40 and $60. The exercise price of a
one-year European call option is $55. The risk-free interest rate
is 5% per annum.
Construct a binomial tree to show the payoff of the call option
at the expiration date. (5%)
Based on the binomial tree model, what is the value of the call
option? (15%)
Address the relation between the binomial...
A stock price is currently $50. It is known that at the end of one year...
A stock price is currently $50. It is known that at the end of
one year it will be either $40 and $60. The exercise price of a
one-year European call option is $55. The risk-free interest rate
is 5% per annum.
a. Construct a binomial tree to show the payoff of the call
option at the expiration date.
b. Based on the binomial tree model, what is the value of the
call option?
c. Address the relation between the...
A stock price is currently $50. It is known that at the end of one month...
A stock price is currently $50. It is known that at the end
of one month it will be either $55 or $45. The risk-free interest
rate is 6% per annum with continuous compounding. What is the value
of a one-month European call option with a strike price of
$48?
A stock price is currently $50. It is known that at the end ofone year...
A stock price is currently $50. It is known that at the end of
one year it will be either $40 and $60. The exercise price of a
one-year European call option is $55. The risk-free interest rate
is 5% per annum. Construct a binoamial tree to show the payoff of
the call option at the expiration date. (5%) Based on the binomial
tree model, what is the value of the call option? (15%) Address the
relation between the binomial...
A stock price is currently $50. It is known that at the end of two months...
A stock price is currently $50. It is known that at the end of
two months it will be either $53 or $48. The risk-free interest
rate is 10% per annum with continuous compounding. Use no arbitrage
arguments. a)
Whatisthevalueofatwo-monthEuropeanputoptionwithastrikepriceof$50?
b) How would you hedge a short position in the option?
:A stock price is currently $50. It is known that at the end of six months...
:A stock price is currently $50. It is known that at the end of
six months it will be either $52 or $48. The risk-free interest
rate is 5% per annum with continuous compounding.
What is the value of a six-month European call
option with a strike price of $50?
Verify that no-arbitrage arguments and risk-neutral
valuation arguments give the same answers.
.
A stock price is currently $50. It is known that at the end of two months...
A stock price is currently $50. It is known that at the end of
two months it will be either $53 or $48. The risk-free interest
rate is 10% per annum with continuous compounding. What is the
value of a two-month European call option with a strike price of
$49?
A stock price is currently $50. It is known that at the end of three months,...
A stock price is currently $50. It is known that at the
end of three months, it will be either $55 or $45. The risk-free
interest rate is 12% per annum with continuous compounding. What is
the value of a three-month European call option with a strike price
of $51?
A stock price is currently $20. It is known that at the end of one month...
A stock price is currently $20. It is known that at the end of
one month that the stock price will either increase to 25 or
decrease to 18. The risk-free interest rate is 12% per annum with
continuous compounding. The hedge portfolio is a long position in Δ
shares of stock plus one short Euorpean call option with strike
price of $15 and expiration in 1 month. Using the no-arbitrage
method, what is the present value of this hedge...
A stock price is currently $40. It is known that at the end of one month...
A stock price is
currently $40. It is
known that at the end of one
month it will be either
$42 or $38. The
risk-free interest rate
is 8% per annum
with continuous compounding.
Use put-call parity to solve the value of the corresponding
put option.
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