MindMap Gallery Derivative CFA Level 2
The mind map derived from CFA Level 25%-10% introduces the knowledge of pricing valuation and contingent clause valuation of forward commitments. I hope this mind map will be helpful to you.
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This is a mind map about plant asexual reproduction, and its main contents include: concept, spore reproduction, vegetative reproduction, tissue culture, and buds. The summary is comprehensive and meticulous, suitable as review materials.
This is a mind map about the reproductive development of animals, and its main contents include: insects, frogs, birds, sexual reproduction, and asexual reproduction. The summary is comprehensive and meticulous, suitable as review materials.
derivative 5%-10%
Pricing Valuation of Forward Commitments
forward
Spot holding arbitrage model carry arbitrary model
Pricing
The target does not generate cash flow
arbitrage
Forward arbitrage cash and carry arbitrary
Borrow money to buy spot, short forward contract, and sell the underlying asset at maturity
reverse cash and carry
The borrowed assets are sold immediately, and the funds are lent to earn interest. Long forward contracts, and the underlying assets are purchased at maturity.
Target generates cash flow
Present value of PVC holding costs
PVB holding income present value
PVC-PVB=net cost of carry
Valuation
The monetary value of a forward contract at a certain time point t after signing and before expiration.
Beginning of period
Midterm
The current price S at time t minus the forward price determined at the beginning of the period discounted to the price at time t
End of term
The underlying assets are stocks and discrete dividends are distributed
Pricing
Valuation
D is for dividen
The underlying assets are fixed income and discrete coupons
Pricing
C is coupon
Valuation
Equity Index Forward
Pricing
Valuation
Forward rate agreement FRA, underlying asset: interest rate
concept
The buyer of the FRA fixes the interest rate on future borrowings
Long position fixed payer, fixed payer, floating float receiver
a×b FRA
a is the maturity date of the agreement, b is the loan settlement date
Pricing
Find the forward interest rate
Valuation
When t=a
NP is notional principal
when t<a
Step 1: Calculate the newly signed FRA interest rate, which is the forward price
Step Two: Calculate FRA Value
Futures future
Fixed income futures, only pricing
Features
Bond prices are usually net
Full price = Net price Accrued interest
According to the cheapest deliverable principle, it is necessary to ensure that the delivery price of deliverable bonds is the same
Actual delivery price = futures price × conversion factor, CF
Pricing
Accrued interest
Full price
formula
Full spot price = full futures price
Swap
interest rate swap
plain vanilla interest rate swapplain vanilla interest rate swap
One party pays a fixed payment and one party pays a floating payment.
There is no exchange of nominal principal at the beginning of the period, the same currency
Interest netting
Pricing
A fixed interest rate causes the contract value to be 0 at the beginning of the period
Pricing is to find the fixed interest rate
fixed rate is swap rate
D is the discount factor
Valuation
Principle: A fixed-rate bond and a floating-rate bond are valued separately and subtracted.
method 1
Method 2
currency swap
in principle
The price difference between bonds of two different currencies must be unified into the same currency
Long on bonds denominated in Currency A Short on bonds denominated in Currency B
Notional principal is exchanged at both the beginning and end of the period
Interest payments are not netted
Pricing
D is the discount factor
Formula and interest rate swap
F is the period coupon rate
Valuation
The difference between the two discounted cash flows
equity swap
An agreement to conduct cash flow swaps based on the income performance of specific equity assets and the agreed interest rate within a certain period in the future.
Loss on swap in or swap out
type
Equity return versus fixed interest rate
Equity Earnings vs. Floating Rates
Equity income versus another equity income
Pricing
Valuation
Receive fixed income and pay equity income to one party
Receive floating amount and pay equity income to one party
Equity and equity swaps
Contingent Valuation
Binary tree pricing
stock binary tree
Valuation steps
According to the no-arbitrage principle, the weighted price calculated by the two branches = the risk-free interest rate investment price, and the probability of rise and fall is calculated.
Calculate option value on each leg
American options need to confirm whether to exercise in advance at the node
weighted option value discount
American options
American options have early exercise problems
The underlying asset is an American call option that does not pay dividends.
Will not exercise rights in advance
The underlying asset is an American put option that pays no dividends.
Exercise in advance
The underlying asset is an American option that pays dividends
Early exercise of deep in-the-money put or call options is advantageous
Optimal hedging ratio = option price change/asset price change
interest rate binary tree
The probability of rise and fall is 0.5, and the others are the same as the stock binary tree.
BSM model
hypothesis
Cannot exercise rights in advance
Price changes are lognormally distributed, consistent with geometric Brownian motion
Rate of return using continuous compounding
Risk-free interest rate lending
The underlying asset volatility is a known constant
frictionless
Model conclusion
The probability of a call option being exercised at expiration
The probability of a put option being exercised at expiration
Call options are used to buy stocks with leverage
Put options short the stock and buy the zero-coupon bond
European stock options or currency options that pay dividends
Holding gains reduce the value of call options and increase the value of put options
implied volatilityimplied volatility
Estimating stock price volatility through the BSM model
Other options
European option on futures
Ignore margin and mark-to-market
Replace S0 in BSM model
Interest Rate Option FRA
swaptions
Greek alphabet
Delta (First order derivative of price)
The shorter the time, the steeper the
nature
at the money, call option delta is approximately equal to 0.5, put option delta is approximately equal to -0.5
delta hedging
The number of options is greater than the number of shares when hedging
Gamma (Second derivative of price)
call and put are the same
Hedging
Nonlinear tool hedges gamma to 0
Linear tools hedge delta to 0
gamma risk
price gap
Vega (volatility partial derivative)
call and put are the same
Theta (time partial derivative)
Rho (interest rate deflection)
long call rho>0 long put rho<0