期货及远期定价工具

分类： Uncategorized
- August 31, 2026
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Calculate theoretical futures prices, implied rates, and basis spreads based on cost-of-carry model

Pricing Model

Calculate the theoretical futures/forward price based on the cost-of-carry model for different asset classes.

$
%
Annualized risk-free interest rate
%
Annualized dividend yield
days
=
years
Theoretical Futures Price
$101.76
F = S × e(r-q)×t = $100.00 × e(4.50% - 1.50%) × 0.247
Basis
+$1.76
Futures Price - Spot Price
Annualized % Basis
+3.00%
Annualized percentage difference
Carrying Cost
$1.76
Net cost of carrying position to maturity
Fair Value Status
Theoretical
Current calculation is theoretical

Calculate the implied financing rate based on the observed futures price and the current spot price.

$
$
%
Annualized dividend yield
days
=
years
Implied Risk-Free Rate
5.60%
r = ln(F/S)/t + q = ln($102.00/$100.00)/0.247 + 1.50%
Implied Financing Cost
$2.00
Total implied cost of financing
Rate vs Benchmark
Unknown
No benchmark rate provided
Basis
+$2.00
Futures Price - Spot Price
Implied Annualized % Basis
+4.10%
Annualized percentage difference

Analyze the basis (difference between futures and spot prices) across different expiration dates to identify term structure and potential trading opportunities.

$
%
%

Futures Contracts

Contract Expiry Date 距到期日数 Futures Price Theoretical Price Basis Annual % Basis 合理价值 Actions
30
$
$100.75 +$0.75 +3.00% Fair
60
$
$101.25 +$1.25 +2.50% Fair

Term Structure & Basis Analysis

Analysis Summary

The term structure is in contango (upward sloping), which is typical in a normal market where carrying costs exceed income yield. The rate of increase is consistent with the cost-of-carry model.

No significant arbitrage opportunities detected based on the current inputs. All contracts are priced close to their theoretical values.

Market Data Reference

The following market rates are provided for reference only. For actual trading, please use the most up-to-date market data from authoritative sources.

Benchmark Interest Rates
USD SOFR 5.31%
USD 3M Treasury 5.42%
USD 3M LIBOR 5.50%
EUR €STR 3.90%
GBP SONIA 5.19%
Major Indices Dividend Yields
S&P 500 1.43%
Dow Jones 2.03%
NASDAQ 100 0.78%
FTSE 100 3.85%
DAX 3.27%
Commodities Storage Costs (Approx.)
黄金 0.25-0.50%
白银 0.50-1.00%
原油 1.00-3.00%
天然气 2.00-5.00%
Agricultural 3.00-7.00%

Understanding Futures & Forward Pricing

Futures and forward contracts are priced based on the cost-of-carry model, which accounts for the cost of holding the underlying asset until the contract's expiration date. The relationship between spot and futures prices is determined by interest rates, dividends/yields, storage costs, and convenience yields.

Cost-of-Carry Model Explained

The cost-of-carry model calculates the theoretical futures price based on the current spot price adjusted for all costs and benefits of holding the underlying asset until expiration:

For financial assets (stocks, indices):
F = S × e(r-q)×t
For currencies:
F = S × e(r-rf)×t
For commodities with storage costs:
F = S × e(r+s)×t
For commodities with convenience yield:
F = S × e(r+s-y)×t
F = Futures price S = Spot price r = Risk-free interest rate q = Dividend yield rf = Foreign risk-free rate s = Storage cost y = Convenience yield t = Time to maturity (in years)

The Basis

"Basis" refers to the difference between the futures price and the spot price (Basis = Futures - Spot).

  • Positive basis (contango): Futures price > Spot price. This is the typical state when carrying costs exceed yields.
  • Negative basis (backwardation): Spot price > Futures price. This occurs when convenience yields or other benefits of holding the physical asset exceed carrying costs.
  • Basis convergence: As the contract approaches expiration, the basis converges to zero (or delivery costs in physical delivery contracts).

Arbitrage and Fair Value

The cost-of-carry model provides a theoretical "fair value" for futures prices. If market prices deviate significantly:

  • Futures overpriced: Sell futures, buy spot (cash and carry arbitrage)
  • Futures underpriced: Buy futures, short sell spot (reverse cash and carry)
  • Arbitrage limitations: Transaction costs, margin requirements, borrowing constraints, and short-selling restrictions may limit perfect arbitrage

Asset-Specific Considerations

Equity Index Futures

For equity indices, dividend yields reduce the cost of carry. Index futures pricing must account for all expected dividends during the contract period. In practice, the dividend estimate is often an annualized yield based on projected payments.

Currency Futures

Currency futures reflect interest rate differentials between two currencies. Higher domestic interest rates typically result in futures trading at a premium to spot (contango), while higher foreign rates lead to futures trading at a discount (backwardation).

Commodity Futures

Commodities often involve physical storage costs and may provide a convenience yield (benefit of holding the physical asset). Seasonal supply/demand patterns can create predictable shifts between contango and backwardation throughout the year.

Interest Rate Futures

These futures typically reflect market expectations of future interest rates. The pricing often relates to forward rate agreements and the shape of the yield curve, rather than simple cost-of-carry calculations.

本工具计算什么

由现货价及持有成本推导的远期或期货合理价格。

公式
F = S × e^((r − q)T)，q 为放弃的收益率或便利收益率
计算示例
现货 100、利率 5%、股息率 2%、一年期：F = 100 × e^(0.03) ≈ 103.05。
何时使用
检视市场报出的远期价相对持有成本是偏贵还是偏平。
常见错误
外汇远期由两种利率共同决定，并非单一利率。只用本地利率会算错远期价，连带掉期定价出错。