r(t) t (current time) which has an

r(t) =
e-?tr(0) + e-?t µ(e?t – 1) + e-?te?s dBs

r(t) = e-?tr(0) + µ(1-e-?t)+ e-?(t-s) dBs

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Call option price of a bond at t
(current time) which has an expiry at time m
such that (tST  (out-of-money) , then the owner will have to
pay a price more than the actual price of the share at time T , resulting in a
loss.However, the option will not be exercised in this case, which is why the
owner pays an extra price for the option.

European put option gives the owner the
right , but not the obligation, to sell the share to the issuer on an agreed
time in the future known as the expiry date (T) at an agreed price called the
strike price (K).While,the writer of the option is obliged to buy the share.

In this case,
the payoff would be C = (K-ST)+

Similarly if K
> ST (in-the-money) then the owner will be selling the share at a
price more than the share price at time T , thereby gain the difference.

Binomial model :

Ina financial market,
a portfolio ( set of assets ,called stocks) which can be bought and sold at
discrete times (1,2,3….) are priced using the binomial model which assumes:

No minimum or maximum units of trading

Short-term interest rate is fixed over the
period of time and is represented by ?

No trading costs or tax

Allowed to borrow/short sell shares

Principle of no-arbitrage applies :