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FRM^®一级金融市场与金融产品备考公式（5）

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发布时间：2021-12-29 10:31

阅读：532次

本文继续为大家介绍FRM®一级风险管理基础的备考公式，以下是第三部分金融市场与金融产品的相关公式（5），一起来看吧。

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Financial Markets and Products

Forward Prices

Forward price when underlying asset does not have cash flows:

F = S(1 + r)T

If F > S(1 + r)T , arbitrageurs will profit by selling the forward and buying the asset with borrowed funds.

If F < S(1 + r)T , arbitrageurs will profit by selling the asset, lending out the proceeds, and buying the forward.

Forward price when underlying asset has cash flows, I :

F = (S – I) × (1 + r)T

Forward price with continuous dividend yield, q:

F = S × [(1 + r) / (1 + q)]T

Forward price with storage costs, U:

F0, T = (S0 + U) × (1 + r)T

Forward price with lease rate, δ

F0, T = S0 × [(1 + r) / (1 + δ)]T

Forward price with convenience yield, Y :

F0, T ≥ (S0 + U) × [(1 + r) / (1 + Y)]T

Backwardation and Contango

Backwardation refers to a situation where the futures price is below the spot price. For this to occur, there must be a significant benefit to holding the asset.

Contango refers to a situation where the futures price is above the spot price. If there are no benefits to holding the asset (e.g., dividends, coupons, or convenience yield), contango will occur because the futures price will be greater than the spot price.

Option Pricing Bounds

Upper bound European/American call:

c≤ S0 ; C≤S0;

Upper bound European/American put:

p ≤ PV(X); P ≤ X

Lower bound European call on non-dividend-paying stock:

c≥ max (S0 – PV(X), 0)

Lower bound European put on non-dividend-paying stock:

p ≥ max (PV(X) – S0, 0)

Put-Call Parity

P= c -S +PV(X)

C=p+S -PV(X)