PRESENTED BY:

ABIHA SYED

AMNA ZAHID

Fixed income or Interest rate options Four basic option strategies Buying a call option on a bond Writing a call option on a bond Buying a put option on a bond Writing a put option on a bond

What is call option? What is premium? Two important things about bond call

options when interest rates rise when interest rates fall

This is the second strategy There are two important things to

notice when interest rates rise and bond prices

fall when interest rates fall and bond prices

rise

What is put option? Two important things to notice here

are: when interest rates rise when interest rates fall

This is the fourth strategy In this case again there are two

important considerations: when interest rates rise and bond prices

fall when interest rates fall and bond prices

rise

Two reasons: Economic reasons for not wring

options Regulatory reasons

In calculating the fair value of an option two models can be used

Binomial model Black-Scholes Model

“The value of the put option increases with the increase in the underlying variance of asses returns”

MATHEMETICAL MODEL

ZERO COUPON BOND HELD TILL MATURITY FACE VALUE $100 N = 2 YEARS PV = $ 80.45 R2 :

P2 = 100/(1+R2)^2

Fearing unexpected deposits withdrawal, the FI manager may be forced to liquidate and sell this two year bond before maturity

Manager may have to sell the bond at the end of the first year

R2 = 11.5%

0 1 2

R2 = 10 R2 = 13.82% or 12.18%

P1 = 100/ 1+r1

@ 13.82% = $87.86 @ 12.18% = $89.41

EXPECTED RATE = 0.5(0.1382) + 0.5(0.1218) =13% EXPECTED PRICE = $88.5

VALUE OF PUT OPTION Max: (88.5 – 87.86, 0) = 0.64 Max: (88.5 – 89.14, 0) = 0

Worth: 0.5(0.64) + 0.5(0) = $ 0.32 P = $ 0.29 or 29 cents

Interest rate increases to 14.82% instead of 13.82%

Max: 88.5 – 87.09, 0 = 1.41

P= 64 cents

The preferred method of hedging that they use is an option on an interest rate futures contract.

FIs hedges by buying put options on futures

If the interest rate rises and bond prices fall, the exercise price higher than the cost of bond

Profit on future options may be made to offset the loss on the market value of bonds held directly in the FIs portfolio.

If interest rates fall while bond prices increase

The buyer of the future option will

exercise the put, and losses on the futures put option are limited to the put premium.

Using Put Option by analyzing Macro hedging. Determine the optimal number of put options to buy to

insulate the FI against moving rates. Use a put option position that generates profits to offset loss in

net worth due to a rate shock. Change in P = (Np * change in p)

(1) Change in P is total change in value of put position in T bonds Np is number of put options on T bond contracts to be

purchased Change in p is change in dollar value for each face value T

bond Change in p = dp/dB *dB/dR * Change in R/ 1+R

(2) For put options, delta has a negative sign since value of put

options fall when bond prices rise. dB/dR shows change in market value of bond, if interest rates

rise by 1 basis points, and it is linked to duration

dB/B = - MD *dR (3) It shows percentage change in bonds price for small change in rates is

proportional to bonds Modified duration. Rearranging it: dB/dR = - MD * B (4) Rewrite eq 2 as: Change in p = [(-d) * (-MD) * B * change in R/1+R] (5) Where change in R/1+R is discounted shock to interest rates The change in Total Value of Put Option(change in P) is: Change in P = Np * [d * MD * B * change in R/1+R] (6) To hedge net worth exposure, we require profits to offset loss of net

worth when rates rise so the number of put options to buy would be: Np = [DA-k*DL ] * A / [d * MD * B]

FI bought one month T bill which is a sterling asset. FI liabilities are in dollars so it hedges the FX risk that

pound sterling will depreciate over the coming years. Pound value less than the current exchange rate , LOSS to

bank on its British T-bill investment when measured in dollar terms.

E.g if pound depreciated from $1.64/1£ to $1.50/1£ , then assets would be worth 150 million instead of 164 million.

To offset this exposure; banks buy 1-month put options on sterling at exercise price of $1.60/1£ , due to this when exchange rate falls to $1.50/1£ , the bank receives 160 million instead of 150 million.

Number of put contracts to buy:Value of T-bill sterling asset/size of each contract

Options have a potential use in hedging Credit risk of an FI. In good economic states, loan portfolio would have low

credit risk and small loan losses. In bad economic states, loan portfolio would suffer

increased credit risk and losses. If there is strong correlation between movement in stock

market index and economic states; selling index futures produces negative outcomes in very good economic states.

So index options may offer better credit risk hedging choice.

The put options reduces credit losses on loan portfolio and even produces net profit in bad economic states.

If constructed correctly the hedged put option can produce a positive return in good economic states as well.