Question

In the one-period binomial model, let *d* be the down
factor and let *r* be the risk-free rate. What will be the
arbitrage opportunity if *d > 1 + r*?

Answer #1

If d > (1 + r) we can create an arbitrage opportunity by borrowing an amount equal to the current stock pirce, S and buying one unit of stock.

Since d > (1 + r); hence, d - (1 + r) > 0

Action at time 0 |
t =
0 |
t =
T |

Borrow @ risk free rate | S | - (1 + r) x S |

Buy stock | - S | d x S |

Total |
0 |
d x S - (1 + r)
S = [d - (1 + r)] x S >0 |

Thus you end up making a riskfree and riskless profit of
**[d - (1 + r)] x S** at t = 1 without any initial
investment. This is the arbitrage profit.

Suppose that you have a stock in the one-period binomial model
with fixed u, d,and r suchthat 0< d <1 + r < u. Suppose
that there are positive numbers p1and q1such that p1,q1<1,
p1+q1= 1, and (1 +r)S0=p1S1(H) +q1S1(T). Show that p1= ̃p and q1=
̃q
.Hint: You know that the risk-neutral probabilities satisfy
these equations as well.

Assume a one-period (annual) binomial model with the following
characteristics: current stock price is $25, the up factor for each
period is 1.05, the down factor for each period is 0.95, and the
risk-free rate is 3 percent.
(a) (4 pts) Draw the binomial tree for the stock with the
appropriate pricing.
(b) (2 pts) What is the current hedge ratio for a European call
for that stock if it has a strike price of $22 and will expire in...

Let the risk-free rate be 10%. Suppose a stock follows a one
period binomial tree structure with a spot value of $100, a value
of $120 in the up state at time 1, and a value of $80 in the down
state at time 1. What is the time 0 price of a put option written
on the stock with a strike of $90?

Consider the following data for a two-period binomial model.
The stock’s price S is $100. After three months, it either goes
up and gets multiplied by the factor U = 1.138473, or it goes down
and gets multiplied by the factor D = 0.886643.
Options mature after T = 0.5 year and have a strike price of K =
$110.
The continuously compounded risk-free interest rate r is 5
percent per year.
Today’s European call price is c and the...

You have a stock in the one-period binomial model such that S0 =
4,S1(H) = 8,S1(T) = 2, and r = 1.5. Show how to extract arbitrage
by explicitly defining a portfolio (X, ∆) such that X0 < 0 while
X1 ≥ 0.

If you were to consider the CAPM as a one-factor model, then the
factor would be the:
rate of inflation.
market risk
premium.
GNP.
risk-free rate.
individual beta of each security or portfolio.

1) Consider a one-period binomial model of 12 months. Assume the
stock price is $54.00,
σ = 0.25, r = 0.04 and the exercise price of a call option
is $55. What is the forecasted price of the stock given an upward
movement during the year?
2) Consider a one-period binomial model of 12 months. Assume the
stock price is $54.00,
σ = 0.25, r = 0.04 and the exercise price of a call option
is $55. What is the...

Exhibit 1. Consider a binomial world in which the current stock
price of 80 can either go up by 10 percent or down by 8 percent.
The risk-free rate is 4 percent and the call exercise price
80.
-----SHOW ALL WORK
6. Consider the information given in Exhibit 1. Assume the
one-period binomial model. What is the hedge ratio?
7. Consider the information given in Exhibit 1. Assume the
one-period binomial model. What is the theoretical value of the
call?...

We have two economic factors F1 and F2 in
a two-factor APT model. We have the following data on three
well-diversified portfolios.
Stock
Expected return
bi1
bi2
A
7%
2
-1
B
17%
1
2
C
12%
1
?
If the risk free rate is 2%, what is stock C's bi2 so
that there is no arbitrage opportunity in the market?
Group of answer choices
0.5
-1
2
1

Price a put option with a one-step binomial tree. Suppose So=50,
X=40, 1+r=1.06. The u factor is 1.4 and the d factor is 0.6. Show
the steps

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 8 minutes ago

asked 8 minutes ago

asked 9 minutes ago

asked 12 minutes ago

asked 15 minutes ago

asked 18 minutes ago

asked 20 minutes ago

asked 24 minutes ago

asked 36 minutes ago

asked 38 minutes ago

asked 38 minutes ago

asked 40 minutes ago