本次英国代写主要为离散时间建模和衍生证券相关的assignment
3.1.时间 0 的股票价格是 S(0) = 100 和每次的利率
步长为 R = 1:5%。
(a) 假设行使价格为 K = 100 的欧式看跌期权
在时间步 T = 10 处以 0 时间 1:3503 的价格交易,而
具有相同行使价和行使时间的欧洲看涨期权交易在
15:0952 在时间 0。如果存在,构建一个套利策略。 (20
分数)
(b) 假设执行价格 K = 120 的欧洲看涨期权是
在时间步 T = 9 执行交易,在时间 0 以 14:7685 的价格交易。
计算欧式期权的无套利时间 0 价格
payo 是 jS(T) Kj(跨式),具有相同的执行价格 K = 120
和运动时间 T = 9。(15 分)
3.2.今天是 2013 年 9 月 17 日。考虑一份远期合约(从
在某个较早的日期)远期价格为 105:65 的风险证券和
交割日 2014 年 4 月 1 日。风险证券今天的价格为 98:40 美元;
假设年复合无风险利率为 4:36%
不变。持有多头头寸的人会赚多少钱
远期合约必须支付(或接收)以关闭今天的头寸(即
是,2013 年 9 月 17 日)?持有人要多少钱
远期合约中的空头头寸必须支付(或接收)以关闭
今天(即 2013 年 9 月 17 日)的位置? (20 分)
3.3.假设利率 r 是常数。设计一个电子表格
计算多头期货头寸的每日盯市现金流
在 30 天内交货的库存。电子表格应采用
(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
在连续 30 天的每一天。 (30 分)
电子表格中使用的公式应在 lyx 文件中给出。
3.4.假设利率 r = 4%(连续复利)是连续的
瞬间。如果今天的股价是 9:14 美元,那么明天的股价是多少
这样,期货中多头头寸的盯市价和交割
3 个月后是 0:54 美元?说明使用的任何公式。 (15 分)
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)