Future Price
Cost of Carry
Stock + Delivery
Cost of Carry Theory
Future Price = Spot Price + Cost of Carry
Convenience Yield
Because future holder claims risk premium, thus, the spot holder has convenience yield.
Cost of Carry Theory #2
Future Price = Spot Price + Cost of Carry - Convenience Yield
Examples
Agricultural futures
F = S(1+r)^t + U + W + T + I - Y
F: Future Price
S: Spot Price
r: Risk-free interest rate
U: Warehouse Cost
W: Damage Cost
T: Transport Cost
I: Insurance Cost
Y: Convenience Yield
t: Time to yield
Agricultural futures
F = S(1+r)^t + U + W + T + I - Y
F: Future Price
S: Spot Price
r: Risk-free interest rate
U: Warehouse Cost
W: Damage Cost
T: Transport Cost
I: Insurance Cost
Y: Convenience Yield
t: Time to yield
Corn spot price is $50/ton at 2020.06, risk-free interest rate is 1.5%. Warehouse cost is $1.2 per month, and should pay on start of month. If you wanna sell it, transport cost is $5 per times.
Q: 2020.10 future price is ?
Agricultural futures
F = S(1+r)^t + U + W + T + I - Y
F: Future Price
S: Spot Price
r: Risk-free interest rate
U: Warehouse Cost
W: Damage Cost
T: Transport Cost
I: Insurance Cost
Y: Convenience Yield
t: Time to yield
Corn spot price is $50/ton at 2020.06, risk-free interest rate is 1.5%. Warehouse cost is $1.2 per month, and should pay on start of month. If you wanna sell it, transport cost is $5 per times.
Q: 2020.10 future price is ?
F = 50*(1 + 1.5%)^4/12 + 1.2 * (1 + 1.5%)^4/12 + 1.2 * (1 + 1.5%)^3/12 + 1.2 * (1 + 1.5%)^2/12 + 1.2 * (1 + 1.5%)^1/12 + 5 * (1 + 1.5%)^4/12
≈ 60.09
Interest Rate futures
F = S(1 + r * t) - M * q * t
F: Future Price
S: Spot Price
r: Risk-free interest rate
M: Face Value
q: Coupon Rate
t: Time to yield
Bonds
Bonds
Bonds
Face Value
Coupon Rate
Maturity Date
Yield
Interest Rate futures
F = S(1 + r * t) - M * q * t
F: Future Price
S: Spot Price
r: Risk-free interest rate
M: Face Value
q: Coupon Rate
t: Time to yield
At 2020/09, 10-year treasury notes face value is $1000, coupon rate is 3.125%, spot price is $1050 and risk-free interest rate is 0.75%.
Q: 2021/09 future price is ?
Interest Rate futures
F = S(1 + r * t) - M * q * t
F: Future Price
S: Spot Price
r: Risk-free interest rate
M: Face Value
q: Coupon Rate
t: Time to yield
At 2020/09, 10-year treasury notes face value is $1000, coupon rate is 3.125%, spot price is $1050 and risk-free interest rate is 0.75%.
Q: 2021/09 future price is ?
F = 1050*(1 + 1.5% * 12/12) - (1000 * 3.125% * 6/12) * (1 + 1.5%)^12/12 - (1000 * 3.125% * 6/12) * (1 + 1.5%)^6/12
≈ 1034.149
Equity Index futures
F = S(1 + (r - d) * t)
F: Future Price
S: Spot Price
r: Risk-free interest rate
d: dividend rate
t: Time to yield
FX futures
F = S(1 + (r - rf) * t)
F: Future Price
S: Spot Price
r: Risk-free interest rate
rf: Foreign Risk-free interest rate
t: Time to yield
Basis
Basis
Spot Price - Future Price
Spread
Spread
Future Price - Spot Price
Spread
Future Price - Spot Price
Yes, Spread = -Basis
Next Time
Trade Strategy
Future Price
By Chia Yu Pai
Future Price
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