Finance Assignment

This document is a finance assignment that covers various topics such as arbitrage, premium calculation, Black Scholes model, and exercise price. It provides step-by-step solutions and explanations for each question. The assignment is suitable for college and university students studying finance.

FINANCE
ASSIGNMENT

1
By student name
Professor
University
Date: 25 April 2018.
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Contents
Question 1...................................................................................................................................................3
Question 2...................................................................................................................................................4
Question 3...................................................................................................................................................5
Question 4...................................................................................................................................................6
References...................................................................................................................................................7
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Question 1
Given:
S(JPY/GBP) = 144.21
S(JPY/USD) = 109.50
S(USD/GBP) = 1.3099
Arbitrage Process
Path 1 USD>JPY>GBP>USD
Sell $ 500,000 at the rate given S(JPY/USD), getting (500000*109.5)
JPY 54750000
Sell JPY 54750000 at the rate given S(JPY/GBP), getting (54750000/144.21)
GBP 379654.67
Sell GBP at the rate given S(USD/GBP), getting (379654.67*1.3099)
USD 497309.652
Loss from arbitrage = 500000-497309.652 = USD 2690.348
Path 2 USD>GBP>JPY>USD
Sell $ 500,000 at the rate given S(USD/GBP), getting (500000/1.3099)
GBP 381708.527
Sell GBP 381708.527 at the rate given S(JPY/GBP), getting
(381708.527*144.21)
JPY 55046186.67
Sell JPY 55046186.67 at the rate given S(JPY/USD), getting
(55046186.67/109.50)
USD 502704.90
Gain from arbitrage = 502704.90-500000 = USD 2704.90
Therefore, in the given case, path 2 helps in making the arbitrage profit of USD 2704.90
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Question 2
The premium is calculated by the formula as shown below
((F-S)/S)*100*12/n
where, F = Forward Rate, S = Spot Rate, n = period
a
.
Particular
s Calculation Result
1 month ((1.3055-1.3087)/1.3087)*100*12/1 -2.93% discount
3 month ((1.3008-1.3087)/1.3087)*100*12/3 -2.41% discount
6 month ((1.2946-1.3087)/1.3087)*100*12/6 -2.15% discount
b
.
Particular
s Calculation Result
1 month ((0.7660-0.7641)/0.7641)*100*12/1 2.98%
Premiu
m
3 month ((0.7688-0.7641)/0.7641)*100*12/3 2.46%
Premiu
m
6 month ((0.7724-0.7641)/0.7641)*100*12/6 2.17%
Premiu
m
c. The results from part a and part b suggest that USD is trading at a discount whereas CAD is trading
at a premium. The USD is appreciating against CAD whereas the CAD is depreciating against the USD
(Alexander, 2016).
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Question 3
Exercise Price = USD 0.7000/AUD
Time period = 210 days
Forward Rate = USD 0.7100/AUD
Interest Rate of USD = 2.5% p.a.
Interest Rate of AUD = 2% p.a.
Volatility = 11.25%
The Black Scholes model formula has been shown below:
d1 = (1/(σ*√T)) * [Ln(S/E)+(r+ (σ^2)/2)*(T)]
Where, T = Time for maturity, S = Current / Spot Price, E = Strike / Exercise Price,
r = risk free interest rate, σ = Price volatility
Here in the given case, S is missing for which the calculation has been shown below
F/S = ((1+ eUSD)/(1+ eAUD))^T
or, 0.7100/S = [(e*0.025)/(e*0.02)]^(210/360)
or, 0.7100/S = [(e*0.005)]^(210/360)
or S = 0.7079
Now, E= 0.7000, S = 0.7079, r = 2%, σ =11.25%, T = 210/360
Now, putting the above values to find out the value of d1
d1 = (1/(σ*√T)) * [Ln(S/E)+(r+ (σ^2)/2)*(T)]
d1 = (1/(0.1125*√(210/360)) * [Ln(0.7079/0.7000)+(0.02+ (0.1125^2)/2)*(210/360)]
d1 = 0.3093
d2 = d1 - σ√T
d2 = 0.3093-0.0859
d2 = 0.2234
N(d1) = 0.6179
N(d2) = 0.5793
C= SN(d1) − (Ke^(−rT)) * (Nd2)
C = 0.7079*0.6179 - (0.70/e^0.002*(210/360))*0.5793)
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C = 0.3029 (Choy, 2018)
Question 4
Exercise Price = USD 0.6500/NZD
Time period = 140 days
Forward Rate = USD 0.6300/NZD
Interest Rate of USD = 2.5% p.a.
Interest Rate of NZD = 2.25% p.a.
Volatility = 13.5%
The Black Scholes model formula has been shown below:
d1 = (1/(σ*√T)) * [Ln(S/E)+(r+ (σ^2)/2)*(T)]
Where, T = Time for maturity, S = Current / Spot Price, E = Strike / Exercise Price,
r = risk free interest rate, σ = Price volatility
Here in the given case, S is missing for which the calculation has been shown below
F/S = ((1+ eUSD)/(1+ eNZD))^T
or, 0.6300/S = [(e*0.025)/(e*0.0225)]^(140/360)
or, 0.7100/S = [(e*0.0025)]^(140/360)
or S = 0.6294
Now, E= 0.6500, S = 0.6294, r = 2.25%, σ =13.5%, T = 140/360
Now, putting the above values to find out the value of d1
d1 = (1/(σ*√T)) * [Ln(S/E)+(r+ (σ^2)/2)*(T)]
d1 = (1/(0.135*√(140/360)) * [Ln(0.6294/0.6500)+(0.0225+ (0.135^2)/2)*(140/360)]
d1 = -0.0190
d2 = d1 - σ√T
d2 = -0.0190-0.0842
d2 = -0.1032
N(d1) = 0.8023
N(d2) = 0.8944
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P= SN(d1) − (Ke^(−rT)) * (Nd2)
P = 0.6294*0.8023 - (0.65/e^0.0225*(140/360))*0.8944)
P = 0.072
References
Alexander, F. (2016). The Changing Face of Accountability. The Journal of Higher Education, 71(4), 411-
431.
Choy, Y. K. (2018). Cost-benefit Analysis, Values, Wellbeing and Ethics: An Indigenous Worldview
Analysis. Ecological Economics, 3(1), 145. doi:https://doi.org/10.1016/j.ecolecon.2017.08.005
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