Rational Pricing: Mastering Rational Pricing, Decoding Finance's Hidden Value

By Fouad Sabry

What is Rational Pricing

The assumption that asset prices, and consequently asset pricing models, will represent the arbitrage-free price of the asset is known as rational pricing. This assumption is based on the fact that any departure from this price will be "arbitraged away" throughout the process of rational pricing. In addition to being an essential component in the pricing of derivative instruments, this assumption is helpful in determining the value of fixed income securities, notably bonds.

How you will benefit

(I) Insights, and validations about the following topics:

Chapter 1: Rational pricing

Chapter 2: Arbitrage

Chapter 3: Derivative (finance)

Chapter 4: Financial economics

Chapter 5: Black-Scholes model

Chapter 6: Real options valuation

Chapter 7: Forward contract

Chapter 8: Binomial options pricing model

Chapter 9: Convertible bond

Chapter 10: Valuation (finance)

Chapter 11: Risk-neutral measure

Chapter 12: Swap (finance)

Chapter 13: Bond valuation

Chapter 14: Arbitrage pricing theory

Chapter 15: Fixed income arbitrage

Chapter 16: Business valuation

Chapter 17: Asset pricing

Chapter 18: Lattice model (finance)

Chapter 19: Real business-cycle theory

Chapter 20: Bootstrapping (finance)

Chapter 21: Replicating portfolio

(II) Answering the public top questions about rational pricing.

(III) Real world examples for the usage of rational pricing in many fields.

Who this book is for

Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of Rational Pricing.

• Language: English
• Publisher: One Billion Knowledgeable
• Release date: Feb 4, 2024

Book preview

Chapter 1: Rational pricing

In financial economics, rational pricing is the notion that asset prices will represent the arbitrage-free price of the asset, as any divergence from this price will be arbitraged away. This assumption is crucial to the pricing of derivative instruments and is useful for pricing fixed-income securities, specifically bonds.

Arbitrage is the technique of exploiting an imbalance between two or more marketplaces. Where this disparity can be exploited (i.e., after transaction costs, storage costs, transport costs, dividends, etc.), the arbitrageur can lock in a risk-free profit by simultaneously buying and selling in both markets.

Arbitrage generally ensures that the law of one price holds; it also equalizes the prices of assets with identical cash flows and determines the price of assets with predictable future cash flows.

On all markets, the same asset must trade at the same price (the law of one price). If this is not the case, the arbitrator will:

Purchase the asset on the market with the lower price while concurrently selling it (short) on the market with the higher price.

handover the asset to the purchaser and receive the increased price.

With the proceeds, pay the seller on the cheaper market and keep the difference.

The price of two assets with identical cash flows must be the same. If this is not the case, the arbitrator will:

Sell the asset with the higher price (short sale) and acquire the asset with the lower price concurrently.

He will purchase the less expensive asset with the profits from the sale of the more expensive asset, pocketing the difference.

use the cash flows from the cheaper asset to fulfill his obligations to the buyer of the costly asset.

A future-priced asset must trade today at the future price reduced by the risk-free rate.

This condition can be considered as an application of the preceding condition, where the two assets in question are the delivered asset and the risk-free asset.

(a) if the discounted future price is greater than the price today:

The arbitrageur offers to deliver the asset at a future date (i.e., sells forward) and purchases it with borrowed funds today.

The arbitrageur hands up the underlying asset and receives the agreed-upon price on the delivery date.

The borrower then repays the lender the principal plus interest.

Arbitrage profit is the difference between the agreed price and the amount refunded (i.e. due).

(b) when the discounted future price is less than the price today:

The arbitrageur promises to pay for the asset at a future date (buys forward) while simultaneously selling the underlying asset (short) today; he invests (or banks) the proceeds.

On the maturity date, he redeems the investment, which has grown at the risk-free rate.

Afterwards, he gets delivery of the underlying asset and pays the agreed-upon amount using the matured investment.

Arbitrage profit equals the difference between the maturity value and the agreed price.

Point (b) is only possible for individuals who possess the asset but have no immediate need for it. In the event that short-term demand exceeds supply, resulting in backwardation, there may be few such parties.

Additionally see Fixed income arbitrage and Bond credit rating.

Fixed-rate bonds may be priced using the rational pricing approach. Here, each cash flow on the bond can be matched by trading in either (a) a multiple of a zero-coupon bond, ZCB, corresponding to each coupon date, and of equivalent credit worthiness (if possible, from the same issuer as the bond being valued) with the corresponding maturity, or (b) a strip corresponding to each coupon and a ZCB for the return of principal on maturity. Consequently, if the cash flows can be repeated, the price of the bond must equal the total of each cash flow discounted at the same rate as each ZCB (per #Assets with identical cash flows). If this were not the case, arbitrage would be available and the price would return to its ZCB-based level. The procedure is as follows:.

Where the price of the bond is misaligned with the current value of the ZCBs, the arbitrageur could purchase the bond at a discount:

Finance her purchase of whichever of the bond or the total amount of ZCBs was less expensive.

by selling short the other

utilizing the coupons or zeroes as needed to meet her cash flow obligations

Consequently, her profit would equal the difference between the two prices.

The pricing formula is then P_{0}=\sum _{{t=1}}^{T}{\frac {C_{t}}{(1+r_{t})^{t}}}

, where each cash flow