Commodities, Forex & Crypto

Q1 (12)

(a) Derivation (6) Assume: no arbitrage, frictionless market, can borrow/lend at $r$, storage cost paid, asset held only for financing (no convenience yield), continuous compounding. (1 for assumptions)

Cash-and-carry replication: today borrow $S$, buy 1 unit spot, and prepay storage. At $T$ deliver into the futures.

• Cost of borrowed cash grows to $Se^{rT}$. (1)
• Storage adds cost that grows as $Se^{uT}$ (treated as continuous proportional carry). (1)
• Combined carry: $S e^{(r+u)T}$. (1) By no-arbitrage the futures price must equal the total carry cost, else risk-free profit exists: (1) $F = S\,e^{(r+u)T}$ (1)

(b) (3) $(r+u)T = 0.06 \times 0.5 = 0.03$. F = 2000\,e^{0.03} = 2000 \times 1.030455 = \2060.91$. (3)

(c) (3) Market $= 2080 >$ fair $2060.91$ → futures overpriced. (1) Cash-and-carry arbitrage:

• Borrow $2000, buy gold spot, pay storage; short the futures at 2080. (1)
• At $T$ deliver gold, receive 2080, repay carry 2060.91 → risk-free profit \approx \19.09$/oz. (1)

Q2 (11)

(a) (4)

• Base currency = first currency in the pair; the one being bought/sold (priced). (1)
• Quote currency = second currency; the price is expressed in it. (1)
• Pip = smallest standard price increment, $0.0001$ for most pairs ($0.01$ for JPY pairs). (1)
• Profit $= N \times \Delta \times (\text{pip size})$ in quote currency (positive for correct direction). (1)

(b) (4) Pip move $= (1.0912 - 1.0850)/0.0001 = 0.0062/0.0001 = 62$ pips. (2) Profit = 100000 \times 62 \times 0.0001 = 100000 \times 0.0062 = \620$. (2)

(c) (3) USD/INR: USD is base, INR is quote → quote tells how many rupees per 1 USD. (1) A depreciating rupee means more rupees needed per dollar → the quote number rises (e.g. 83 → 85). (1) Standard convention because USD is the global reserve/base currency. (1)

Q3 (9)

(a) (4) EUR/INR $= \dfrac{\text{EUR}}{\text{USD}} \times \dfrac{\text{USD}}{\text{INR}}$; USD cancels. (2) $= 1.0900 \times 83.20 = 90.688$. (2)

(b) (5) Dealer quotes 91.20, synthetic (true) $= 90.688$ → dealer's EUR is overvalued in INR. (1) Arbitrage: sell EUR to the dealer for INR at 91.20, then buy EUR back synthetically via USD at 90.688. (2) Per 1000 EUR: receive $91200$ INR, cost to rebuy $= 90688$ INR → profit $= 512$ INR. (2)

Q4 (12)

(a) (6)

function computeHash(index, prevHash, timestamp, data, nonce):
    return SHA256(index + prevHash + timestamp + data + nonce)

function mineBlock(block, difficulty):
    target = "0" * difficulty          # required leading zeros
    nonce = 0
    while True:
        h = computeHash(block.index, block.prevHash,
                        block.timestamp, block.data, nonce)
        if h[:difficulty] == target:
            return nonce, h            # valid block found
        nonce += 1

Marks: correct hash-of-fields concept (2), loop incrementing nonce (2), leading-zero target / difficulty check (2).

(b) (3) Hot wallet = connected to internet (exchange/app), convenient but exposed. (1) Cold wallet = offline (hardware/paper), safer for storage. (1) You secure the private key because coins live on the blockchain; whoever holds the key can move the coins — losing the key loses access permanently. (1)

(c) (3) Bitcoin: digital store of value / peer-to-peer cash, Proof-of-Work. (1) Ethereum: programmable smart-contract platform (dApps), now Proof-of-Stake. (1) Altcoin = any cryptocurrency other than Bitcoin. (1)

Q5 (9)

(a) (4) (1 mark each: mechanism + a risk)

• Fiat-collateralised (e.g. USDC): backed 1:1 by dollars in reserve; risk = reserve/custodian trust & audits.
• Crypto-collateralised (e.g. DAI): over-collateralised with crypto; risk = collateral crash / liquidation cascade.
• Algorithmic: supply expands/contracts by algorithm; risk = de-peg / death spiral (e.g. UST). (4th mark: any coherent 4th risk point or clear structure.)

(b) (5) Annualised vol $= \sigma_{daily}\sqrt{n} = 0.04 \times \sqrt{365}$. (2) $\sqrt{365} = 19.105$; $= 0.04 \times 19.105 = 0.7642 = 76.4\%$. (2) Equity index: $0.01\times\sqrt{252}\approx 15.9\%$ — crypto is roughly 4–5× more volatile. (1)

Q6 (7)

• MCX standardises contracts (lot size, quality/grade, delivery, tick) so trading is fungible & liquid. (2)
• Clearing house acts as central counterparty, collects initial + maintenance margin to guarantee performance. (2)
• Daily mark-to-market: gains/losses settled each day so no large accumulated exposure builds up. (2)
• This reduces counterparty/default risk by ensuring losses are covered before they compound. (1)

[
  {"claim":"Gold fair futures = 2000*e^0.03 ≈ 2060.91","code":"import sympy as sp\nF=2000*sp.exp(0.03)\nresult=abs(float(F)-2060.909)<0.01"},
  {"claim":"Arbitrage profit per oz ≈ 19.09","code":"import sympy as sp\nF=2000*sp.exp(0.03)\nprofit=2080-float(F)\nresult=abs(profit-19.091)<0.01"},
  {"claim":"EUR/USD long 100k, +62 pips = $620","code":"pips=(1.0912-1.0850)/0.0001\nprofit=100000*pips*0.0001\nresult=abs(pips-62)<1e-6 and abs(profit-620)<1e-6"},
  {"claim":"EUR/INR cross rate = 90.688","code":"cross=1.0900*83.20\nresult=abs(cross-90.688)<1e-6"},
  {"claim":"Cross arb profit per 1000 EUR = 512 INR","code":"cross=1.0900*83.20\nprofit=1000*(91.20-cross)\nresult=abs(profit-512)<1e-6"},
  {"claim":"Annualised crypto vol = 0.04*sqrt(365) ≈ 76.4%","code":"import sympy as sp\nv=0.04*sp.sqrt(365)\nresult=abs(float(v)-0.7642)<0.001"}
]