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DRM PROJECT - TASK A
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StockCoal India
Synthetic call strategy
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TickerCOALINDIACall Price9.15
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Time3 monthsPut Price5.85
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Spot₹ 384.35Risk Free Rate 5.60%
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Atm options
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Put call parity
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(All taken at atm)P+S0 =C+Ke-rt
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Long Stock + Long Put
(So+P)Call PriceMetricTrade 1 (Aug-Aug)
Trade 2 (Aug-Sep)
Trade 3 (Sep-Oct)
Trade 4 (Oct-Nov)
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Date
Price (So+P)
Price (c)Start Date21-Aug-2529-Aug-251-Oct-2529-Oct-25
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8/21/2025384.0012.10End Date28-Aug-2530-Sep-2528-Oct-2521-Nov-25
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8/22/2025380.309.30Call Entry12.108.1018.457.50
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8/25/2025385.8511.55Call Exit 7.9519.508.209.15
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8/26/2025378.307.20Call P&L-4.1511.40-10.251.65
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8/28/2025380.157.95Call Return (%)-34.30%140.74%-55.56%22.00%
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8/29/2025380.658.10
Synthetic Entry (S+P)
384.00380.65394.35387.85
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9/1/2025383.756.65Synthetic Exit380.15395.80397.25384.35
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9/2/2025385.9515.05Synthetic P&L -3.8515.152.90-3.50
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9/3/2025395.6519.90
Synthetic Return (%)
-1.00%3.98%0.74%-0.90%
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9/4/2025397.3020.60Option Expiry30-Sep-2528-Oct-2525-Nov-2530-Dec-25
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9/8/2025392.9011.30
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9/9/2025393.8010.90
For each of the one-month windows, the ATM call option and the synthetic call (constructed using Long Stock+Long Put) nearly moved in the same direction, consistent with put-call parity.
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9/10/2025397.7512.65
But their percentage returns differed significantly. The synthetic call required much higher initial capital (S+P) compared to the actual call premium. Even when the P&L on both positions was similar in direction, the call delivered far higher percentage returns due to leverage, while the synthetic return remained small and more risk averse.
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9/11/2025399.2020.10
Small deviations also appeared because Coal India stock options are illiquid. Settlement-based option pricing, bid-ask spreads, and dividend effects created mild parity violations.
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9/12/2025400.2020.45
Overall, the call outperformed the synthetic on a percentage basis in most months, showing that buying the actual call is more capital-efficient than replicating it synthetically. Higher ROC for actual call.
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9/15/2025400.6014.60
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9/16/2025401.6514.75
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9/17/2025405.6022.60
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9/18/2025399.0012.75
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9/19/2025400.3513.10
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9/22/2025400.5513.45
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9/23/2025399.9013.40
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9/24/2025398.7011.80
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9/25/2025398.3511.20
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9/26/2025395.008.55
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9/29/2025394.1518.80
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9/30/2025395.8019.50
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10/1/2025394.3518.45
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10/3/2025389.209.40
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10/6/2025387.758.95
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10/7/2025390.5510.00
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10/8/2025387.958.25
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10/9/2025389.209.05
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10/10/2025390.359.25
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10/13/2025387.407.70
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10/14/2025386.807.20
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10/15/2025390.108.15
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10/16/2025393.459.65
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10/17/2025394.659.35
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10/20/2025396.459.85
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10/21/2025396.9510.20
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10/23/2025398.509.95
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10/24/2025399.909.40
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10/27/2025402.5510.85
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10/28/2025397.258.20
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10/29/2025387.857.50
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10/30/2025393.5516.80
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10/31/2025394.5023.05
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11/3/2025394.4022.50
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11/6/2025379.0013.00
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11/7/2025381.8514.30
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11/10/2025387.2016.85
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11/11/2025388.6517.55
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11/12/2025392.3519.70
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11/13/2025389.0517.45
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11/14/2025392.8019.70
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11/17/2025393.7019.75
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11/18/2025389.8017.00
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11/19/2025384.9013.85
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11/20/2025385.5014.00
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11/21/2025384.359.15
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Method:
Three trades taken and compared/analysed unlike the two year task where rollling trades were taken.
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