Expected Return Analysis

In the case of Forward buying and Call Option buying at the point of 1030 and assuming that the probability of Spot rate at a maturity will be as shown below

Spot rate	1010	1020	1030	1040	1050
Probability	20%	20%	20%	20%	20%

> Forward Buying

(20%x(1010-1030))+(20%x(1020-1030))+(20%x(1030-1030))+(20%x(1040-1030))+(20%x(1050-1030))=0

> Call Option Buying

When Spot rate is 1010, 1020 and 1030, gain from Call Option is 0.

(20%x(1040-1030))+(20%x(1050-1030))=6

There is problems in pricing!!

Spot rate	1010	1020	1030	1040	1050
Probability 20% 20% 20% 20% 20%

What if the assumption on probability was wrong?

Price changes as per the change of the probability

Spot rate	1010	1020	1030	1040	1050
Probability	10%	25%	30%	25%	10%

When Spot rate are 1010, 1020 and 1030, gain from Call Option is 0.

(25% x(1040-1030)) + (10% x (1050-1030)) = 4.5

Spot rate	1010	1020	1030	1040	1050
Probability	5%	15%	60%	15%	5%

When Spot rate are 1010, 1020 and 1030, gain from Call Option is 0.

(15% x(1040-1030)) + (5% x (1050-1030)) = 2.5

As the volatility of Spot rate gets lower, Call Option price falls

- In contrary, as the volatility of Spot rate gets higher, Call Option price rises

If to apply same theory to Put Option,
Volatility rises => Put Option price rises
Volatility falls => Put Option price falls

※ “Option price (regardless of Call or Put) moves toward same direction of the Volatility”

Historic Volatility: Trend of Spot rate in the past

Implied Volatility: Market view on the trend of Spot rate in the future => used to decide Option price

- Quantify using a standard probable deviation in the probability: 7% or 9%, etc.

- Probability that Spot rate will be within 1 of standard deviation at the maturity: 60%

- Probability that Spot rate will be within 2 of standard deviation at the maturity: 95%

- In reality, the implied volatility is traded in the market: 1 month ~ 12 months, bid/ask are existent

- can calculate Option price through Expected Return Analysis using the implied volatility