Forward contract price
FP = S0 × (1 + Rf)^T

forward overpriced:borrow money ⇒ buy (go long) the spot asset ⇒ go short the asset in the forward
forward underpriced:borrow asset ⇒ short (sell) spot asset ⇒ lend […]

CDS spread ≈ (1 – RR) × POD
POD:Probability of default
RR:recovery rate

credit spread on bonds = yield – LIBOR
Credit spreadsは hazard rates や loss given defaultと正の相関があり, recovery ratesとは負の相関があります。

upfront […]

Structural Models
value of risky debt = value of risk-free debt − value of put option(strike price equal to the face value of debt)
value of risky debt = value of risk-free debt − CVA
Therefore, the value of […]

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Probability of survivall is the probability that the bond does not default.
PS(t) = (1 – hazard rate)^t
PD(t) = hazard rate × PS […]

バリュー
Vcall = Vstraight − Vcallable
Vput = Vputable − Vstraight […]

CIRモデル

CIRモデル（Cox‐Ingersoll‐Ross Model）とは、金利の期間構造を […]

Pure expectations hypothesis
純粋期待仮説（Pure expectations hypothesis）とは […]

Interpolated rate = rate for lower bound + (interpolated rate − lower bound)(higher bound rate − lower bound rate) / ( upper bound − lower bound)

Swap sprea […]

build-up method=the risk-free rate+ the equity risk premium+the small stock premium+a company-specific risk premium+industry risk premium