3.1.时间 0 的股票价格是 S(0) = 100 和每次的利率

(a) 假设行使价格为 K = 100 的欧式看跌期权

15:0952 在时间 0。如果存在，构建一个套利策略。 (20

(b) 假设执行价格 K = 120 的欧洲看涨期权是

payo 是 jS(T) Kj（跨式），具有相同的执行价格 K = 120

3.2.今天是 2013 年 9 月 17 日。考虑一份远期合约（从

3.3.假设利率 r 是常数。设计一个电子表格

（连续复利）固定利率 r 和每日股票价格
S(0); S(1); : : : ; S(30) 作为输入。为简单起见假设交易发生

3.4.假设利率 r = 4%（连续复利）是连续的

3 个月后是 0:54 美元？说明使用的任何公式。 (15 分)

Discrete Time Modelling and Derivative Securi-
ties
Coursework Assignment 3
3.1. The time 0 stock price is S(0) = 100 and the interest rate over each time
step is R = 1:5%.
(a) Suppose that European puts with strike price K = 100 to be exer-
cised at time step T = 10 trade at the price of 1:3503 at time 0, while
European calls with the same strike price and exercise time trade at
15:0952 at time 0. Construct an arbitrage strategy if one exists. (20
marks)
(b) Suppose that European calls with strike price K = 120 to be ex-
ercised at time step T = 9 trade at a price of 14:7685 at time 0.
Compute the arbitrage-free time 0 price of a European option whose
payo is jS(T) Kj (a straddle) with the same strike price K = 120
and exercise time T = 9. (15 marks)
3.2. Today is 17 September 2013. Consider a forward contract (which started
on some earlier date) on a risky security with forward price \$105:65 and
delivery date 1 April 2014. Today’s price of the risky security is \$98:40;
and the annually compounded risk-free interest rate is 4:36%, assumed
constant. How much money would the holder of a long position in the
forward contract have to pay (or receive) to close the position today (that
is, on 17 September 2013)? How much money would the holder of a
short position in the forward contract have to pay (or receive) to close the
position today (that is, on 17 September 2013)? (20 marks)
3.3. Assume that the interest rate r is constant. Design a spreadsheet to
compute the daily marking-to-market cash ow of a long futures position
on a stock with delivery in 30 days. The spreadsheet should take the
(continuously compounded) constant interest rate r and daily stock prices
S(0); S(1); : : : ; S(30) as inputs. Assume for simplicity that trading occurs
on each of the 30 consecutive days. (30 marks)
The formulae used in the spreadsheet should be given in the lyx le.
3.4. Assume that the interest rate r = 4% (continuously compounded) is con-
stant. If today’s stock price is \$9:14, what will be tomorrow’s stock price
such that the marking-to-market for a long position in futures with deliv-
ery in 3 months is \$0:54? State any formulae used. (15 marks)