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

Question

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.

Robert · Accepted Answer

In this case �, �, �, �, �, � 
In this case 
0
080
S
=.
, 
081
K
=.
, 
008
r
=.
, 
005
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
-
¢
=..´.´.=.

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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