Derivatives Flashcards
Calculate the hedge ratio.
Hedge ratio = option value rise - option value fall / (underlying price rise - underlying price fall)
Calculate the call option using PV of the portfolio and current value.
value of hedged portfolio = hedged ratio * underlying price increase - value of option increase
Hedged raio * current price - call option = value of hedged portfolio / interest rate
Solve call option
Calculate the risk netural probability of a 2 steps binomial model.
risk netural probability of up = ( 1 + risk free rate - down ) / (up - down)
up and down is the change in price.
eg up = 1.2 and down = 0.9
Calculate the put-call parity.
and also under continuously componded basis.
Call option price + Strike price / (1 + r) ^T = put option price + spot price
Fiduciary call = Protective put
under the continuously componded basis the (1+r)^T becomes
e ^ (r * T)
Define swaps and interest rate swaps.
Swaps can be replicated by series of forward contracts (FRAs)
Swaps are equivalent to a set of options.
An interest rate swap is the same as buying a series of calls and selling a series of puts, with the exercise rate same as fixed rate on the swap.
Caculate the (interest rate) swap price of the contract using present value factor.
Equivalent to sell fixed bond and buy floating rate bond.
Price of (interest rate) swap = 1 - Last discount factor / Sum of discount factors
Then annualized the Price
Price of swap annualized = price of swap * 360 / payment days
eg if quarterly payment: payment days = 90 days = multiple by 4.
where discounts factors = Present value factor
How to convert a floating rate payment into present value factor?
eg floating rate payment of 7% in 180 days using (30/360). What is the present value factor?
Present value factor = 1 / (1 + float rate * days / 360)
= 1 / (1 + 0.07 * 170 / 360)
= 0.9662
Calculate the forward price and value of equity forward.
Forward price = Spot price + Net costs of carry
Forward price = Spot price at start * (1 + r)^T - FV(CF)
FV(CF) = Future value of coupon payments
Vt =PVt * (Ft -F0)
Calculate the forward price and value of equity index forwards.
Forward price = Spot price * e ^ [(interest rate + cost of carry - Dividend yield) *months in contract / 12]
Vt = (Ft - F0) /(e^ [r*(T-t)]ost
Calculate the future contract price for fixed income.
Future contract price = 1/ Conversion factor * [(Bond price at start + Accured interest at start - PV(All coupon interest) * (1 + interest rate) ^ (month /12) ) - Accured interest at terminal]
Calculate the value of the swap.
Value of the swap = Value of fixed rate bond - value of floating rate bond
Calculate the market value of equity swap.
Value of equity swap = Value at end / Value at start * notional amount - PV of bond (Par = notional amount)
Calculate the value of future contract of a treasury note.
Quoted Futures Price = 1 / conversion factor * (Inital price + accured interest - PV(Future cashflow) * (1 + risk free rate) ^ (Months / 12) - Accured interest on expire
Draw the pay off diagram for Short/Long/Put/Call option.
Long Call | Long Put
Short Call | Short Put
Out of money / In monery |In money / Out of money
