速寫 Day25


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今日日文單字:

  • 見るに堪(た)えない ─ 不忍直視
  • NというN ─ 強調
  • Nぶる/ぶって/ぶったN ─ 裝作
  • Nぶり ─ 從…
  • Vる/Nだに ─ 光是
  • こととて ─ 因為…
  • 昔(むかし)ほど恐れるに足らない ─ 與以前相比不足為懼
  • ご心配には及びません ─ 不必擔心

稍微的筆記

ch34 Pricing Financial Forwards and Futures:
Value of a Forward Contract:
  • The forward price at every moment in time is computed to prevent arbitrage, the value at inception of the contract must be zero.
  • If we denote the obligated delivery price after inception as K, then the value of long contract on an asset with an annual dividend yield of q is computed as: \(\dfrac{S}{(1+q)^T}-\dfrac{K}{(1+r)^T}\)
  • If interest rates rise, then the underlying assets will fall in value. That is, there’s a loss on both futures and forwards contracts. However, with futures, a loss from an asset price decrease will be recognized immediately (due to daily settlement). In that regard, a forward contract is more desirable and would be price higher.
ch35 Commodity Forwards and Futures:
  • Commodities prices tend to be mean-reverting.
Energy:
    1. Crude oil: easy to transport.
    1. Natural gas: is expensive to store.
    1. Electricity: is not generally a storable commodity. Due to that, arbitrage opportunities do not exist with electricity. In other words, futures prices on electricity can be much more volatile than financial futures.
Commodity Arbitrage:
  • The makets for those commodities that are storable are called as carry markets.
  • cash-and-carry arbitrage:
    1. \(F_{0,T}=(S_0+U)\times(1+r)^T\), where U implys storage costs.
    1. \(F_{0,T}=(S_0-I)\times(1+r)^T\), where I implys income(or we can say the storage costs are negative.)
    1. The commodity forward price with an active lease market is expressed as: $$F_{0,T}=S_0\times[\dfrac{(1+r)}{(1+\delta)}]^T$$, where \(\delta \) implys lease rate.
    1. The forward price including a convenience yield is calculated as: $$F_{0,T}\geq (S_0+U)\times[\dfrac{(1+r)}{(1+Y)}]^T$$, where Y implys annualized convenience yield.
  • Convenience Yield (便利孳息) : The nonmonetary benefit of holding excess inventory. (which is only relevant (有效) when a commodity is stored. e.g., in a carry market.)
  • Lease rate is similar to the dividend payment in a financial forward, which can be negative.
Futures Prices and Expected Spot Prices:
  • \(E(S_T)=F\dfrac{(1+X)^T}{(1+r)^T}\), where X implys expected return on futures position.
  • Recall that Systematic risk is a function of the correlation btw the return on the market versus the underlying asset. If the correlation is positive, then X should exceed r.
  • Normal backwardation (正常倒退): If the correlation is positive, X > r, thus \(E(S_T)>F\).
  • Contango (期貨升水): If the correlation is negative, \(E(S_T)<F\).

今日其他進度:

  • 日文N1文法、N1題目
  • FRM ebook ch34 35
  • 一堆的動畫

我會繼續努力的。




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