A financial institution has just sold 1,000 seven-month European call options on the Japanese yen suppose that the spot exchange rate is 0.80 cents per yen, the exerciser price is 0.81 cents per yen,...

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A financial institution has just sold 1,000 seven-month European call options on the Japanese yen suppose that the spot exchange rate is 0.80 cents per yen, the exerciser price is 0.81 cents per yen, the risk-free interest rate in the United State is 8% per annum, the risk-free interest rate in Japan is 5% per annum, and the volatility of then yen is 15% per annum. Calculate the delta, gamma, vega, theta, and rho of the financial institution’s position. Interpret each number.

Answered Same DayDec 24, 2021

Answer To: A financial institution has just sold 1,000 seven-month European call options on the Japanese yen...

Robert answered on Dec 24 2021
137 Votes
In this case �, �, �, �, �, �
In this case
0
080
S
=.
,
081
K
=.
,
008
r
=.
,
00
5
f
r
=.
,
015
=.
s
,
05833
T
=.

(
)
2
1
21
ln(080081)008005015205833
01016
01505833
0150583300130
d
dd
./.+.-.+./´.
==.
..
=-..=-.

12
()05405()04998
NdNd
=.;=.
The delta of one call option is
00505833
1
()0540505250
f
rT
eNde
-
-.´.
=´.=.
.
2
1
2
000516
1
11
()03969
22
d
Ndee
-/
-.
¢
===.
pp
so that the gamma of one call option is
1
0
()
0396909713
4206
08001505833
f
rT
Nde
ST
-
¢
.´.
==.
.´.´.
s
The vega of one call option is
01
()08005833039690971302355
f
rT
STNde
-
¢
=..´.´.=.
The theta of one call option is...
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