Options Basics

Q1 (10 marks)

(a) For a call: intrinsic value = max(Spot − Strike, 0); time value = premium − intrinsic. Spot = 1020.

• 1000 call: Spot > Strike ⇒ ITM. Intrinsic = 1020−1000 = 20. Time value = 38−20 = 18. (2)
• 1020 call: Spot = Strike ⇒ ATM. Intrinsic = 0. Time value = 25−0 = 25. (2)
• 1040 call: Spot < Strike ⇒ OTM. Intrinsic = 0. Time value = 15−0 = 15. (2)

(b) At the 1020 strike the call and put are both ATM (intrinsic = 0), so both premiums are pure time value. The call premium (25) exceeds the put premium (22) largely because of the cost-of-carry / interest effect (put–call parity: C − P = S − K·e^(−rt) > 0 when S = K and r > 0). A call buyer defers paying for the stock, giving the call extra value over the put. (2 marks for identifying both are pure time value; 2 marks for the carry/parity reasoning.)

Q2 (10 marks)

(a) Long call breakeven = Strike + Premium = 1040 + 15 = ₹1,055. (2)

(b) Per-share P/L = max(S−1040,0) − 15; multiply by lot 50. (2 each)

• S = 1030: payoff = max(−10,0)=0; P/L per share = −15; total = 50×(−15) = −₹750.
• S = 1055: payoff = 15; P/L = 15−15 = 0; total = ₹0 (breakeven).
• S = 1080: payoff = 40; P/L = 40−15 = 25; total = 50×25 = +₹1,250.

(c) Maximum loss = premium paid = 15×50 = ₹750 (occurs at any S ≤ 1040). Maximum profit is theoretically unlimited since the stock price can rise without bound. (2)

Q3 (10 marks)

(a) Short put: writer keeps premium if S ≥ strike; loss grows as S falls below strike. Breakeven = Strike − Premium = 1000 − 14 = ₹986. Payoff = +premium for S ≥ 1000, declining linearly below, max profit = premium (₹14/share), large loss potential down to S=0. (3)

(b) Per-share P/L for short put = 14 − max(1000−S, 0). (≈1.3 each)

• S = 1010: put expires worthless; P/L = +14/share ⇒ 50×14 = +₹700.
• S = 990: intrinsic = 10; P/L = 14−10 = +4/share ⇒ +₹200.
• S = 960: intrinsic = 40; P/L = 14−40 = −26/share ⇒ 50×(−26) = −₹1,300.

(c) An American put can be exercised by the holder at any time; the writer may be assigned early, e.g. when the put goes deep ITM (S well below strike) or around a dividend / when interest makes early exercise optimal — the holder exercises to capture intrinsic value immediately. A European put can only be exercised at expiry, so the writer cannot be assigned before the expiry date. (3)

Q4 (12 marks)

(a) PCR (OI) = Total Put OI / Total Call OI. Total Put OI = 350000+280000+220000+140000+90000 = 1,080,000. Total Call OI = 120000+150000+200000+340000+410000 = 1,220,000. PCR = 1,080,000 / 1,220,000 = 0.885 (≈0.89). (3)

(b) PCR < 1 means more call OI than put OI, generally read as mildly bearish-to-neutral / cautious sentiment (heavier call writing above spot). Caveat: PCR is a contrarian/context indicator — extreme readings can signal reversals, and OI alone doesn't distinguish buyers from writers, so it should not be used in isolation. (3)

(c) Resistance ≈ 22200 — highest call OI (4,10,000); heavy call writing above spot caps upside. Support ≈ 21800 — highest put OI (3,50,000); heavy put writing below spot cushions downside. (3)

(d) Buying the 22100 call gives a bullish position with limited loss = premium paid. Selling the 21800 put is also bullish but carries large (near-unlimited to zero) downside risk if the market falls. For a "limited-loss" preference, the long 22100 call is more consistent. (3)

Q5 (8 marks)

• (a) FALSE — deep ITM options are dominated by intrinsic value; time value is small. (2)
• (b) FALSE — a European call is generally worth the same as an American call on a non-dividend stock (early exercise of a call is not optimal); it is never worth more, but "can never be worth more" as a blanket loses no value — the given reasoning about being cheaper is what matters. Statement claims it "can never be worth more" which is essentially true for calls; the reasoning ("because it cannot be exercised early") is flawed — accept FALSE with correct explanation that early exercise adds no value for calls. (2) (Award full marks for TRUE-with-correct-reasoning OR FALSE-with-correct-reasoning; key point: American ≥ European always, equal for non-dividend calls.)
• (c) TRUE — at expiry there is no time left (time value = 0) and OTM means intrinsic = 0. (2)
• (d) TRUE — a buyer can lose at most the premium paid; downside is capped. (2)

[
  {"claim":"1000 call time value = 18","code":"premium=38; intrinsic=max(1020-1000,0); tv=premium-intrinsic; result = (tv==18)"},
  {"claim":"1040 call breakeven = 1055","code":"be=1040+15; result = (be==1055)"},
  {"claim":"Long 1040 call P/L at S=1080, lot 50 = 1250","code":"S=1080; pl=(max(S-1040,0)-15)*50; result = (pl==1250)"},
  {"claim":"Short 1000 put P/L at S=960, lot 50 = -1300","code":"S=960; pl=(14-max(1000-S,0))*50; result = (pl==-1300)"},
  {"claim":"PCR (OI) approx 0.885","code":"puts=350000+280000+220000+140000+90000; calls=120000+150000+200000+340000+410000; pcr=Rational(puts,calls); result = (abs(float(pcr)-0.885)<0.005)"}
]