Derive Flashcards
WHat is the forward price?
The price you’re going to sell something for in the future
@ expiration, what is the formula for the value of a Short position forward contract?
Value = Forward price - market price
I was going to buy it for the forward price, minus what it is actually worth
WHat are some of the rules of derivative arb trading?
Never use your own money, do not take price risk, sell a forward contract, discount expected profit to review it today
What is carry>
Buying an instrubment and the forward
Explain the simple version of derivative trade when the future spot price = current spot rice + risk free rate
First, buy the instrument using borrowed money. Then sell the instrument in one period using to get the intiaul investment + the risk free rate. You then gotta pay back the money you borrowed, so minus the inital investment and risk free rate
What should the profit be if future spot prices = current + risk free rate
0
How do you profit if a forward price is OVER the spot price plus risk free rate
In these situations, you have to borrow against the profit you are going to make. So if the forward price is 110, and the spot price in one year will be 109, you discount that 1$ by the risk free rate, and you get that upfront, as profit today.
Not a question, but think of all this like a term deposit, if the forward price of the cash you would receive on a 100$ deposit @ 2% is 103, you could SELL that option to someone to get that 103 in the future, but only end up paying 102. Easy
See question
If the spot price at T+.25 is 101, when there is a 10% r, is there value to a forward contract in one year @ 110. What is the process to work this out?
No, you would have to product that 101 by 1+r ^.75, then subtract that by the forward price. Then discount BACK to that T+.25 to get the value then
Why would you want to pay for a forward contact above that of the market price
Is the carry cost paying interest, or recieving interest?
Paying
Do you add or subtract the value of dividends/positive cash flows from the value of the spot price to determine the future price? And why
Subtract that. The dividends are not enjoyed by the long side, the person taking the forward price - he should be compensated for not getting those divs, so the forward price is lowered.
Formula for continuous compounding Forward price and when we we use it?
Spot 0 e^(r-div)*T
The continuous formula is used for indexes like SP500 when the dividends could come in everyday
How to find forward price on an equity contract?
Forward price = (Spot price - PV of Divs ) * 1+r^T
If you wanted to find the value of a forward contract at some point prior to expiration, what is the formula, and what does it mean?
Forward value= (Spot price t - PV of Divs ) - (Future Price / (1+r)^(T-t)
This is finding the spot price at a given moment, then subtracting the present value of the future price
LIBOR is quoted on how many days a year?
360
Equity and bonds are quoted on how many days a year?
365
Does the long or short party recieve the underlying instrument at expriation?
The long party.
If interest rates increase, what happens to the price of the forward contract. What happens if divs/cash flows increase?
It increases as well. If divs increase, the value decreases
What happens if the market price of a forward is below that which you calculate? How would you benefit? Explain
A reverse cash-and-carry arbitrage strategy is only worthwhile if the futures price is cheap relative to the spot price of the asset. Reverse cash-and-carry arbitrage is a market-neutral strategy combining a short position in an asset and a long futures position in that same asset. Its goal is to exploit pricing inefficiencies between that asset’s cash, or spot, price and the corresponding future’s price to generate riskless profits.
If the market price is ABOVE the real forward price, is there a cash and carry or reverse cash and carry situation?
Normal. The futures contract must be theoretically expensive relative to the underlying asset or the arbitrage will not be profitable. It combines the purchase of a long position in an asset such as a stock or commodity, and the sale (short) of a position in a futures contract on that same underlying asset.
Does the long party revieve fixed or floating payments in a LIBOR FRA?
Floating
Do we quote in dirty or clean price? What do they mean and formula
Dirty price which includes accrued interest. Days since last pmt/days in period * pmt
At the end of the forward, who gives the underlying over?
The long party
Why would someone enter in a forward rate agreement?
They think interest rates will go up
Explain the process of a forward rate agreement IF interest rates rise?
So, you enter into an agreement with your bank to pay a loan of 5% in 60 days. In 60 days the loan starts, but interest rates have increased to 6%. So that means you still have to pay the bank back the loan at 6%, expect, the bank gives you the 1% difference discounted at 6%.
For FRA, what does the X . Y mean. Eg, a loan for 2x6
That means the FRA loan will start in 2 30 day periods, and will last for 4 months beyond that (6 months total)
What does cheapest to deliver mean? And what does it mean for the forward buyer
Since many bonds can fit the criteria of one tied to a forward agreement, you pick the one that is cheapest to deliver. It means that the forward buyer does not have to pay the orginal forward price, but pays the forward price times the conversion factor of the underyling bond
What is the price of the underlying future formula with accrued interest?
It is the clean price of the bond (1+r) - accured interest - coupons
WHen does a Future contract have value?
Not at the end of the trading day, only during. COS IT IS MARKED TO MARKET EVERYDAY BRO
What are differences in the risk free rate attributable to? Across countries
Changes in inflation across countries
What is a straddle?
Buying put AND call options with the same price at the same time
For swaps, what is paid at initiation?
Nothing
What happens to the value of a swap immediatley after each cash flow?
Marked back to $0 in value
What is someone trying to do when they enter into a swap?
Mitigate interest rate risk
How do you price a forward contract with currencies, what is the process, formula etc.
So the formula is
Spot (either rate or dollar amount) * $ risk free rate / foreign risk free rate.
So you are effectively compounding the numerator, then discounting back to the denominator
Or you can also do
Spot rate * (1+risk free local / 1+risk free foreign)
When working out forward rates or sport rates at some point between the strike time, what should we remember
The subnoted t is the same for the Spot and the Future.
For example, the Value t = Forward t - Forward 0
Differences in formula between value or price for forwards?
Value = (Forward t - Forward 0)
General rule for value of contracts?
Spot - Present value of forward
Explain the process of a currency swap.
You exchange notional at inception, then the fixed rate of interest in the currency you borrowed each period, then exchange the notional amount at expiry
How to calculate the fixed rate in a swap?
Fixed rate = 1- Last discount rate / sum of all discount rates
How to calculate discount rate/factor
1 / 1+ rate * % of year (like 25% for quarterly)
How to calcualte how much is paid each period during a swap
Is the fixed rate * percentage of year (25% for quarterly) * notional amount
How do you calc the value of a swap (fixed vs floating) and why does this work
Is the PV of all the fixed payments (PMT * discount factor) then minus the the next iteration of LIBOR payment. 1+Libor * discount factor.
Subtract them from one another to get value.
Only the next floating payment can be calcualted, so we use that only
In simple terms, how do you calculate the value of a swap?
It is the present value one set of flows against the end value of the notional times variable rate
The PV value is just determined using the discount factor.
Why woukd you want to get more duration exposure, and how would you acheive this?
If you think IR is going to go down, and then you can buy into fixed rate swaps. This will give you more duration than the floating rate counterpart
What is the hedge ratio, how do you calcualte it?
It is the delta hedge, or how effected your portfolio of derivatives is to changes in prices of the underlying.
It is calculated by
Call Price if Up move - Call price if Down move / Spot price up - spot price down
WHat does this symbol mean in option trading and how do we calculate it π
Is it the probablity of an up movement on the binomial option tree.
It is calcuated by Risk free Rate - spot at down move (d) / spot at up move - spot move down
How do we calculate value of an option, and what are some things we have to take into consideration
c0 = [π c+ + (1 - π) c-] / (1 + r) (Remember PV)
BUT Remember you need to determine the value of C+. c+ could have a value of 0 if the exercise price is higher than the spot price.
c+ formula. What happens if exervise is higher than spot,
Spot - Exercise. c+ = 0
p+. What happens if exervise is higher than spot,
Exercise - Spot. p+ has value
What does u really mean in option pricing
The multiplier of the spot value if the price of the underlying goes up
How to calc value of euro option? Full process with all formulas please using binomial
So, you find the value at the end of each node based on the U and D factors. Spot times u^2 for a 2 period model etc. Then you subtract the exercise price from it, rememeber (spot - X ,0 = Value).
Next, for an upper node, you times it by pie, and the lower by 1-pie to get the weighted value , then discount back 1 period to get the value at the node prior. You repeat this process for all nodes. This will give you value
What is the hedge ratio, what is its greek name, and what does it mean?
THe hedge ratio is Call + - Call - / Spot + - Spot -.
It is pretty much delta, and shots how much the call price moves based on the change in spot prices.
It is used to netrualise exposure to an underlying by combining other derivative contracts
List and describe each greek.
Delta - hedge ratio, change
Gamm - sort of like convexity, measures rate of change in delta. Only works when the option is NOT deep in or out of the money
Rho - sensitivity of price to risk free rate
Theta - sensitivity of price to time.
Vega - sensitivity of price to volatility
What is a key nuance of theta, and what does it mean
That bonds that are deep in the money have negative theta because there is more opporuntity for the value to decrease rather than increase
Black scholes model? What is it and what are the assumptions of the model
A option valuing model. It assumes: - Underlying follows lognormal distribution - Risk free rate is known and constant - Volatility is known and constant - Frictionless markets - Options are european - Yields are continuously compounded
Do dividends increase or decrease the value of a call option
Decrease
How would one create an synthetic FRA using derivatives, and describe what the output is
If you were long a call interest rate option, and short an interest rate PUT. So you gain when interest rates rise, and lose when interest rates fall, just like an FRA
What does delta hedging the formula mean
It means for every 1$ change in spot, the call price is effected by the delta hedge
To create a delta neutral portfolio, you need 2 things, what are they?
Short time period
Low market vol
What is the formula for creating a delta neutral portfolio using the delta hedge ratio? What is unique about the delta that you need to remember?
The # stocks = - (Delta) * # of options
The delta is only poisitve for CALLs or long strategies. Short strategies will be negative e.g. - (-Delta)
What the heck is a swaption? And if i was to go into a reciever swaption, what does that mean? And why would i enter such a thing?
A swaption is an OPTION to buy a swap. A reciever swaption is a reciever fixed rate swaption that you would enter if you think interest rates are going to go DOWN, because you are paying a floating rate, you want that nice and now
What is a payer swaption>
A payer swaption is you pay a fixed rate, recieve floating
How would you synethetically create a Recieve floating swap?
You would combine a Long Recievier swpation + short payer swaption.
Because you will recieve the fixed rates, then have to pay the floating rates because the other party would exercise the payer swaption
Would a higher exercise price on a put option increase or decrease the value?
Increase it homie, it is more likley to be put
If there is a small change in the price of a stock, how do you hedge against this?
You add the hedge delta and hedge gamma. This accounts for both small and large changes. Gamma helps with small changes
Key difference between equilibrium model and arb free model? Fixed income
Arb model is ensuring that you cant arb derivatives, equilibirum is future = spot
How to find up factor and down factor
Up factor is S+/S and down factor is S-/s
How to calculate how many future contracts you need to increase or decrease exposure to an equity.
(Beta equity / beta contract) * (value of position you are trying to increase/decrease exposure /value per contract )
Fixed income question. -Duration * (change in spread) is what?
The change in price if a bond is downgraded, upgraded
Read this for swaps
https://www.analystforum.com/t/swaps-for-dummies/81579
Explain the effect on duration for pay fixed recieve floating swap
Fixed rate bond has a positive duration.
Floating rate bond has a close-to-zero duration.
Paying fixed meaning you pay out (give away) your duration, and receive 0 duration.
